From owner-philofractal@icd.com Sat May 1 03:33:40 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id CAA05717 for philofractal-list; Sat, 1 May 1999 02:33:30 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp3.mindspring.com (smtp3.mindspring.com [207.69.200.33]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id BAA05442; Sat, 1 May 1999 01:40:41 -0500 Received: from LOCALNAME (user-2iveijl.dialup.mindspring.com [165.247.74.117]) by smtp3.mindspring.com (8.8.5/8.8.5) with SMTP id CAA15803; Sat, 1 May 1999 02:41:02 -0400 (EDT) Date: Sat, 1 May 1999 02:41:02 -0400 (EDT) Message-Id: <1.5.4.16.19990501024033.2977472a@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 01-05-99 (Cave of the Winds) (c) Cc: fractal-art@icd.com Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- May 01, 1999 Fractal enthusiasts: When I launch forth into the world of fractals, I see myself as an explorer, born too late to explore this world and too early to explore other worlds, but at just the right time to explore the world of fractals. And while I explore, I am constantly frustrated by my inability to visualize four spatial dimensions. This inability is curious. Mathematically, the third dimension has no special significance; physically, it has ultimate signif- icance. As far as we can tell, our universe has but three spatial macro-dimensions. True, higher dimensions might exist, but they are wound up so tightly in so tiny a size that they must remain forever far beyond our reach. So in our minds as in our bodies we are bound to three spatial dimensions. We cannot imagine a space of more dimensions; we cannot imagine a space of less without involuntarily adding the missing dimensions around our 2, 1, or zero-dimensional spatial visualization. It is not obvious why this must be so. Perhaps three-dimen- sional space is but a reflection of our own particular state of awareness. It is very comforting to think of space as existing out there all around us. It is not so comforting to suppose that the space that appears so solidly out there might in the end be but a mental construct. Yet there is something instinctively appealing about the idea of man being one with the universe. It is comforting to think that man is part of the universe, and the universe is part of man. If one doubts this, he/she need only to read any New-Age publication. Where do I stand on the issue? My head is with the rational- ists; my heart is with the New-Agers. And with science discovering things that make less and less common sense, who knows what might turn out to be true. The truth of today's fractal, however, is not in doubt. It is a slightly trivial little scene whipped up in a hurry from one of my mysterious MandNewt formulas during a short break in a very busy afternoon. I named the picture "Cave of the Winds" when I thought I saw the mouth of a cave on a ledge overlooking an infinity of nothingness. The parameter file computes in a minute or two on a Pentium. (And who does fractals on anything less?) The JPEG file has been posted in its dataless glory to: and to: The weather both yesterday and today was perfect here at Fractal central. On both days a partly cloudy sky and temperature of 68F 20C made it perfect for searching for fractals. I'll be here again tomorrow with another fractal and another word or two about things mysterious and arcane. Until then, take care, and find a fractal with a friend. Jim Muth jamth@mindspring.com START FORMULA============================================= MandNewt09 {; Jim Muth z=c=pixel: a=z^3+(c-1)*z-c b=p1*z^p2+c-1 z=z-1*a/b p3 <= |a| } END FORMULA=============================================== START PARAMETER FILE====================================== Cave_of_the_Winds { ; 10min on a 486-100, 640x480 reset=1960 type=formula formulafile=mandnewt.frm formulaname=MandNewt09 passes=1 center-mag=1.9899/44.7918/0.09454522/1/112.5 params=-1.050523/-3.727729/1.644841/1.811899/-0.9\ 64431/-1.047105 float=y maxiter=120 bailout=25 inside=bof60 logmap=yes symmetry=none periodicity=10 colors=000BEH<9>16I06I18K<38>Zuz\ <30>iQziPzkOzlNz<4>rYzs_zr`z<2>rbzrczqczqczqdzq\ ezqez<4>phzpizoizoizojzofz<5>nlzmmznnz<6>ntsntm\ <29>onjupl<8>7cX1aY<14>Fg8Df5<38>ymx<29>Xr`CFH } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= Cave_of_the_Winds { ; 10min on a 486-100, 640x480 reset=1960 type=formula formulafile=mandnewt.frm formulaname=MandNewt09 passes=1 center-mag=1.9899/44.7918/0.09454522/1/112.5 params=-1.050523/-3.727729/1.644841/1.811899/-0.9\ 64431/-1.047105 float=y maxiter=120 bailout=25 inside=bof60 logmap=yes symmetry=none periodicity=10 colors=000BEH<9>16I06I18K<38>Zuz\ <30>iQziPzkOzlNz<4>rYzs_zr`z<2>rbzrczqczqczqdzq\ ezqez<4>phzpizoizoizojzofz<5>nlzmmznnz<6>ntsntm\ <29>onjupl<8>7cX1aY<14>Fg8Df5<38>ymx<29>Xr`CFH } frm:MandNewt09 {; Jim Muth z=c=pixel: a=z^3+(c-1)*z-c b=p1*z^p2+c-1 z=z-1*a/b p3 <= |a| } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Sun May 2 01:34:36 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id AAA12445 for philofractal-list; Sun, 2 May 1999 00:33:38 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp1.mindspring.com (smtp1.mindspring.com [207.69.200.31]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id AAA12374; Sun, 2 May 1999 00:21:52 -0500 Received: from LOCALNAME (user-2iveiap.dialup.mindspring.com [165.247.73.89]) by smtp1.mindspring.com (8.8.5/8.8.5) with SMTP id BAA24358; Sun, 2 May 1999 01:21:48 -0400 (EDT) Date: Sun, 2 May 1999 01:21:48 -0400 (EDT) Message-Id: <1.5.4.16.19990502012112.2987be86@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 02-05-99 (Elephant Ring) (c) Cc: fractal-art@icd.com Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- May 02, 1999 Fractal enthusiasts and visionaries: Today's fractal resembles an eight-vaned child's windmill with a fractal elephant-valley type elephant at the tip of each peach- colored vane. I have named the picture "Elephant Ring" because the elephants are arranged in a perfect circle, marching clockwise around the tiny midget at the center. To produce today's image, I mixed 111 parts of Z^11 with 1111 parts of Z, multiplied the mixture by 0.002 and added C. The formula calculated a critical plane; the fractal that resulted was a twisted M-set, which was simply filled with midgets. The particular midget illustrated in today's fractal lies as expected in the East Valley area of its parent fractal. And yes, I did increase the contrast of the image in Photoshop 5.0. I'm not a total purist. The parameter file runs in a few minutes, and even better, the JPEG file has been posted to: and to: We had a high sky today here at Fractal Central, the kind of deep, featureless blue, cloudless backdrop that baseball outfielders so dislike. But though it may not have been perfect for judging the flight of fly balls, it was perfect for seeking fractals. While admiring that deep blue sky this afternoon, I caught sight of two high, white dots, circling each other in tight circles. When I spotted them, I went indoors to get my binoculars, but by the time I found the binoculars, the white dots had vanished and I had to satisfy myself with a 10X daytime view of the planet Venus, which with a clear sky is usually visible to the naked eye in full daylight if one knows where to look. Had I been a believer in alien visitors to earth, I might have suspected two UFO's. But being a skeptic, I suspect a pair of birds, or two escaped balloons. Sad to say, whatever the dots were, we'll never know. With that mystery, we've come to the time to shut down the fractal shoppe, and get some food into my cat, who is rubbing around my legs. I'll be here again tomorrow with fractals and gossip. Until then, take care, and when abducted by aliens, show them your best fractal. Jim Muth jamth@mindspring.com START FORMULA============================================= MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END FORMULA=============================================== START PARAMETER FILE====================================== Elephant_Ring { ; 30min on a 486-100, 640x480 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.99109139950804970/-0.31944810475337320\ /4.690581e+011/1/72.643/-0.193 params=111/11/1111/1/-0.998/0 float=y maxiter=1800 bailout=25 inside=0 logmap=115 symmetry=none periodicity=10 colors=000E0kE0k<3>L0sN0uP2vR4xT6z<4>\ bGzZHzVHzRHzNJzJJzHLzELzANz6Nz2Nz0Pz0Px0Rx0Rv0Tv0Tu0\ Tuzmozpozlkzgizdgz`dzYbxX`uVXqPVoLTkJPgGNeCLbAHZ6GX4\ EbGRgPbkZmqixvszzzzvzzszzoxzkxzgvzdvz`vzZuzVuvRsuNsq\ JsoGqmCqi8og6oe2mb0m`0mX0kV0kT0iP0iN0iL0`R0TV0LZ0Cd4\ 4gA0kE0oH0kL0i<2>XCb`H`bLZePXiVVmZRqbPugNxkLzoJvVesC\ zo0zm0zi0zg0zd0z`0zZ2zV4zT6zP8zNAzJAzGCzEEzAGz8Hz4Jz\ 2Jz4Hz6Gz8EzAEzCCxEAvG8uH8qJ6oL4mN2kP2iR0gT0eT0dV0`\ <4>d0Re0Pg0L<4>q0Cs0As08x00zE0zV0zk0zm0zm0zo0xo0uq0q\ q0ms0is0eu0bu0Zv0Vv0Rx0Nx0Jz0Gz0Cz28z44z40z60z60z80z\ 80zA0zA0zG0zJ4zNCzRJzXRz`Xzddzgkzmszqzzuzzxzzzzzz<2>\ zzuvzuszsqzqmzoizmezmdzk`ziXzgVzgXziZzkZzm`zm`zobzqb\ zsdzsdzuezvezxgzxgzzizzizzkzzmzzmzzozzozzqzzqzzszzsz\ zuzzuzzvzzvzzxzzxzzzzzzzz<3>kzzgzzezzbzzZzzVzzRzxPzu\ LzsHzoEzmAzi6zgkzg } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= Elephant_Ring { ; 30min on a 486-100, 640x480 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.99109139950804970/-0.31944810475337320\ /4.690581e+011/1/72.643/-0.193 params=111/11/1111/1/-0.998/0 float=y maxiter=1800 bailout=25 inside=0 logmap=115 symmetry=none periodicity=10 colors=000E0kE0k<3>L0sN0uP2vR4xT6z<4>\ bGzZHzVHzRHzNJzJJzHLzELzANz6Nz2Nz0Pz0Px0Rx0Rv0Tv0Tu0\ Tuzmozpozlkzgizdgz`dzYbxX`uVXqPVoLTkJPgGNeCLbAHZ6GX4\ EbGRgPbkZmqixvszzzzvzzszzoxzkxzgvzdvz`vzZuzVuvRsuNsq\ JsoGqmCqi8og6oe2mb0m`0mX0kV0kT0iP0iN0iL0`R0TV0LZ0Cd4\ 4gA0kE0oH0kL0i<2>XCb`H`bLZePXiVVmZRqbPugNxkLzoJvVesC\ zo0zm0zi0zg0zd0z`0zZ2zV4zT6zP8zNAzJAzGCzEEzAGz8Hz4Jz\ 2Jz4Hz6Gz8EzAEzCCxEAvG8uH8qJ6oL4mN2kP2iR0gT0eT0dV0`\ <4>d0Re0Pg0L<4>q0Cs0As08x00zE0zV0zk0zm0zm0zo0xo0uq0q\ q0ms0is0eu0bu0Zv0Vv0Rx0Nx0Jz0Gz0Cz28z44z40z60z60z80z\ 80zA0zA0zG0zJ4zNCzRJzXRz`Xzddzgkzmszqzzuzzxzzzzzz<2>\ zzuvzuszsqzqmzoizmezmdzk`ziXzgVzgXziZzkZzm`zm`zobzqb\ zsdzsdzuezvezxgzxgzzizzizzkzzmzzmzzozzozzqzzqzzszzsz\ zuzzuzzvzzvzzxzzxzzzzzzzz<3>kzzgzzezzbzzZzzVzzRzxPzu\ LzsHzoEzmAzi6zgkzg } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Sun May 2 23:33:51 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id WAA20494 for philofractal-list; Sun, 2 May 1999 22:33:57 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from snipe.prod.itd.earthlink.net (snipe.prod.itd.earthlink.net [207.217.120.62]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id WAA20437 for ; Sun, 2 May 1999 22:27:59 -0500 Received: from Peter (sdn-ar-002orportP322.dialsprint.net [168.191.232.228]) by snipe.prod.itd.earthlink.net (8.9.3/8.9.3) with SMTP id UAA29726 for ; Sun, 2 May 1999 20:27:48 -0700 (PDT) Message-Id: <3.0.6.32.19990502202555.007aadd0@earthlink.net> X-Sender: pfjakub@earthlink.net X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.6 (32) Date: Sun, 02 May 1999 20:25:55 -0700 To: philofractal@icd.com From: Peter Jakubowicz Subject: Re: [philofractal] question In-Reply-To: <3.0.3.32.19990420090425.006f57f0@mail.nznet.gen.nz> References: <01be8a62$03af49c0$LocalHost@default> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com Can someone give me an example of a really obscure curve whose tangent is undefined at any point--an ACSII drawing would be appreciated. TIA _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Mon May 3 01:33:56 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id AAA21273 for philofractal-list; Mon, 3 May 1999 00:33:31 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp04.primenet.com (daemon@smtp04.primenet.com [206.165.6.134]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id AAA21159 for ; Mon, 3 May 1999 00:17:38 -0500 Received: (from daemon@localhost) by smtp04.primenet.com (8.8.8/8.8.8) id WAA23236 for ; Sun, 2 May 1999 22:17:21 -0700 (MST) Message-Id: <199905030517.WAA23236@smtp04.primenet.com> Received: from ip-53-009.scf.primenet.com(206.132.53.9), claiming to be "wavdqqrm" via SMTP by smtp04.primenet.com, id smtpd023211; Sun May 2 22:17:16 1999 From: "Kerry Mitchell" To: Subject: Re: [philofractal] question Date: Sun, 2 May 1999 22:09:46 -0700 X-MSMail-Priority: Normal X-Priority: 3 X-Mailer: Microsoft Internet Mail 4.70.1161 MIME-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com Any fractal will work. Take, for example, the Koch curve for example, or the Hilbert curve, or the boundary of the Mandelbrot set, or the Dragon curve, or... Kerry ----------------------------------------------------------------- Kerry Mitchell lkmitch@primenet.com http://www.primenet.com/~lkmitch/ ----------------------------------------------------------------- ---------- > From: Peter Jakubowicz > To: philofractal@icd.com > Subject: Re: [philofractal] question > Date: Sunday, May 02, 1999 8:25 PM > > Can someone give me an example of a really obscure curve whose tangent is > undefined at any point--an ACSII drawing would be appreciated. TIA > > _______ ______ _____ ____ ___ __ _ > post: send message to philofractal@icd.com > unsub: send "unsubscribe" to philofractal-request@icd.com > admin: send comments to philofractal-owner@icd.com _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Mon May 3 01:40:15 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id AAA21277 for philofractal-list; Mon, 3 May 1999 00:33:34 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from bo.nznet.gen.nz (ns1.nznet.gen.nz [203.167.232.34]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id AAA21088 for ; Mon, 3 May 1999 00:05:01 -0500 Received: from packrat.nznet.gen.nz (ms2-31.nznet.gen.nz [203.167.232.161]) by bo.nznet.gen.nz (8.8.7/8.8.8) with SMTP id RAA07385 for ; Mon, 3 May 1999 17:09:04 +1200 Message-Id: <3.0.3.32.19990503170255.006fa554@mail.nznet.gen.nz> X-Sender: packrat@mail.nznet.gen.nz X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.3 (32) Date: Mon, 03 May 1999 17:02:55 +1200 To: philofractal@icd.com From: "Morgan L. Owens" Subject: Re: [philofractal] question In-Reply-To: <3.0.6.32.19990502202555.007aadd0@earthlink.net> References: <3.0.3.32.19990420090425.006f57f0@mail.nznet.gen.nz> <01be8a62$03af49c0$LocalHost@default> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com At 20:25 02/05/99 -0700, you wrote: >Can someone give me an example of a really obscure curve whose tangent is >undefined at any point--an ACSII drawing would be appreciated. TIA > (I) Kiesswetter's Curve. The points of Kieswetter's Curve can be partitioned into four subsets, each of which are affine transformations (scalings, rotations, and reflections) of the entire set. It's easiest definition is as an IFS: Kieswetter { .25 0 0 -.5 0 0 .25 .25 0 0 .5 .25 -.5 .25 .25 0 0 .5 .5 0 .25 .25 0 0 .5 .75 .5 .25 } Not only is it a curve, but it's a function g:[0,1]->R, with the property that: | j j+1 | 1 | g(---) - g(---) | = --- | 4^k 4^k | 2^k for all integers k>=0 and 0<=j<2^k An ASCII drawing of a nowhere-differentiable curve - now _there's_ a challenge! The IFS does the job better, but let's see if I'm up for it... * * * ** * ** * **** * **** *** * ** * *** * ** * * ** **** * ** **** ** ** * ** ** * *** *** * * Naturally, it's a bit fuzzy :-) (II) The Besicovitch-Ursell functions. The most famous of nowhere-differentiable continuous functions is are of course those of Weierstrass (who it must be mentioned got a lot of ribbing from colleagues about his mucking around with such pathalogical monsters). Weierstrass functions are of the form inf f(x) = SUM a sin(b x) k=0 k k For suitable choices of the a's and b's. But this isn't necessarily the most convenient of beasties to work with. Besicovitch and Ursell had the idea of replacing the sine curve with a simple zigzag: First, we define a function g:R->R by g(x)=x for -1/2<=x<1/2 g(x)=1-x for 1/2<=x<=3/2 g(x+2)=g(x) for all x. This is our zigzag function. Now, for 0 X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 03-05-99 (Spiderweb Minibrot) (c) Cc: fractal-art@icd.com Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- May 03, 1999 Fractal enthusiasts: Today was perfectly average here at Fractal Central. I saw no mysterious white dots high in the sky, and no other unexplained aerial phenomena to speculate about. Actually, being an experienced observer of the sky takes a lot of the fun out of the things that appear there. Where some see the space craft of visitors from alien worlds, I see only natural cloud formations, optical effects, astronomical events and man-made artifacts. I sometimes envy those who can glance at the sky and almost at will see aliens scooting around earth's atmosphere in their space ships. It appears that the more one knows about the sky the less the chance the person will see an actual alien space craft. (But aliens are often sighted in fractal land, as a quick trip to ABPF will show.) The sky was partly cloudy today here at the fractal corner. The temperature of 66F 19C was a bit below normal for mid-spring, but perfect for seeking and finding those elusive fractals. Today's fractal illustrates a minibrot caught in a spider web, so I named it "Spiderweb Minibrot". The formula is once again M-Mix4, and the fractal comes from a mixture of Z^2.5 and Z^(-4.5). Despite the brilliance of the colors, I used no third- party graphics program to do this one. The parameter file runs in less than a minute on a Pentium. Nonetheless, the picture file has been posted to: and also to: for the convenience of overworked fractaliers. Things have been a bit slow on the philosophical front lately. I'll see if I can stir up a bit of controversy by tomorrow to liven things up. And I'll also have another semi-glorious fractal to gaze at and then exclaim "wow!" So until then, take care, and may the great fractal watch over you. Jim Muth jamth@mindspring.com START FORMULA============================================= MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END FORMULA=============================================== START PARAMETER FILE====================================== Spiderweb_Minibrot { ; 6min on a 486-100, 640x480 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.17225820462867290/0/6.553424e+008 params=1.5/2.5/3.5/-4.5/-0.87/0 float=y maxiter=1800 bailout=25 inside=0 logmap=41 symmetry=xaxis periodicity=10 colors=000UFGUBAZ75c30hA4mG7<2>tYHvcK\ wiNxmQnkLeeHXbDO`9VcN`h_YrTVzNXuOYlP_fQ`YQbUR<2>fUTY\ cSQeSVjU_XWdUYmU_rTTxSNvRHuPBtO5<5>ZIIYHKbGSfDZjIenN\ l<4>BSw<2>UMg_KbfIYmGTmEOmCJmGO<3>CWg<7>6dxPauf_r\ <12>yoH<8>sxPCyR<14>Tz4<12>hzK<2>KzKCzF5zA<4>8zk<8>F\ zk<2>UzE<12>bzTbzUazU_zUZzU<5>`zZ`zb<18>`zZ`zc\ <22>`zZXzp<7>`z`kzzezlezf<11>`zZuzj<11>jzc } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= Spiderweb_Minibrot { ; 6min on a 486-100, 640x480 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.17225820462867290/0/6.553424e+008 params=1.5/2.5/3.5/-4.5/-0.87/0 float=y maxiter=1800 bailout=25 inside=0 logmap=41 symmetry=xaxis periodicity=10 colors=000UFGUBAZ75c30hA4mG7<2>tYHvcK\ wiNxmQnkLeeHXbDO`9VcN`h_YrTVzNXuOYlP_fQ`YQbUR<2>fUTY\ cSQeSVjU_XWdUYmU_rTTxSNvRHuPBtO5<5>ZIIYHKbGSfDZjIenN\ l<4>BSw<2>UMg_KbfIYmGTmEOmCJmGO<3>CWg<7>6dxPauf_r\ <12>yoH<8>sxPCyR<14>Tz4<12>hzK<2>KzKCzF5zA<4>8zk<8>F\ zk<2>UzE<12>bzTbzUazU_zUZzU<5>`zZ`zb<18>`zZ`zc\ <22>`zZXzp<7>`z`kzzezlezf<11>`zZuzj<11>jzc } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Tue May 4 01:33:54 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id AAA30347 for philofractal-list; Tue, 4 May 1999 00:33:49 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp3.mindspring.com (smtp3.mindspring.com [207.69.200.33]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id XAA30020; Mon, 3 May 1999 23:36:46 -0500 Received: from LOCALNAME (user-2iveijd.dialup.mindspring.com [165.247.74.109]) by smtp3.mindspring.com (8.8.5/8.8.5) with SMTP id AAA19343; Tue, 4 May 1999 00:35:59 -0400 (EDT) Date: Tue, 4 May 1999 00:35:59 -0400 (EDT) Message-Id: <1.5.4.16.19990504003511.29975ed6@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 04-05-99 (Stellar Nursery) (c) Cc: fractal-art@icd.com Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- May 04, 1999 Fractal enthusiasts: When I first saw today's fractal, it reminded me of those photo- graphs of stellar nurseries sent back from the space telescope. Accordingly, I named it "Stellar Nursery". The formula of the fractal is .01(100Z+Z^100)+C, which was achieved with the M-Mix4 formula, of course. To get the astronomical effect, I yielded to temptation and ran the GIF file through a graphics program before converting it to JPEG. But I did little enough alteration so that the image still meets my standards of fractal purity and simplicity. Beginning with today's parameter file, I am listing the calcula- tion time on an average Pentium rather than a 486. It's a logical move, since almost nobody generates fractals on a 486 these days. To convert the Pentium time to the old 486 time, multiply by 6. I had intended on waxing philosophical this evening, but I've been watching TV, where the Cuban baseball team is playing the local Orioles team. Our team is taking another beating, this time 12-3, and in a game we were certain to win. Well, you can't win them all, but you'd like to win at least half. Anyway, the JPEG file of today's fractal has been graciously posted to: also to: The weather today at Fractal Central was imperfect -- low clouds, with occasional drizzle and light rain, and a tempera- ture of 58F 14.5C. But it was perfect for finding a fractal such as today's tapestry of burgeoning stars. Now we've come to the end of the FOTD, but I'll be here again tomorrow. I've got some deep philosophy built up -- about things such as fractals in relation to the meaning of life and the human condition. It's the kind of stuff that gets interes- ting discussions going, but I have to be in just the right state of mind to compose it. I may get it done by tomorrow, or I may not -- check then to see. Regardless, one thing certain is that I'll have another fractal. Until then, take care, and . . . nuts, the game's over . . . we lost 12-6! Jim Muth jamth@mindspring.com START FORMULA============================================= MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END FORMULA=============================================== START PARAMETER FILE====================================== Stellar_Nursery { ; 4-1/2min at 640x480 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.09294912167762445/+0.00143386807667\ 271/1.009587e+007/1/180 params=100/1/1/100/-0.99/0 float=y maxiter=1500 bailout=25 inside=0 logmap=90 symmetry=none periodicity=10 colors=000ADa0Cj2AmC9mA8om6qz0or8rgJtUUvFew5ry0zz\ 0zz1zy5ywAvvFrtFtzJotMlmPggUdaXaW__PbYL60AC8QGG_L\ PdddIgqI8_CDYIIXOMWUQU_WTeaIge8gl0gq0gj0a<2>U0JP0\ DJ08800F03L06Q09X0Cd2Fj5Iq9Lv3MwCOoJPgQQ_YTTeULmW\ FvXJrUOoTTlPXhOWoJ_gMd_OhTPlLQqDTv6Uy0Wo6XeDYYLYP\ T_I__9ga0tb2ma3ga6ba8XaAQaCMaFGaD6gGCa<2>OPJQWDT_\ 8Wd2Wg0Xh0Xh1Xj5Qo1Xj8aOFe2MgAThJY<3>otwtzzqzzowv\ lqojlhhebe_XdUQjUMbPL<2>JCGD8F83D21D9W0Ga0Y0gbC_e\ _ThyLazJWzJOzI<2>2zD0zC0zC0z92z88z6Dz3Jz2Pz1<4>vz\ 0zz0<2>yy0ht0Uo0Fj11e30a60Y9<2>0QI0OL2LO5IQ6GU9DX\ AA_<3>L1lD0rM0oW1l<2>w8bz8d<2>z9YwAWrCUoDTlFQhGOe\ IMaJLYLIWMGTOFLPFPQDTTCWUAYWAbX9eY8h_8la6ob5td3we\ 3zg2zh1zj3zl1zm0to0lq0<2>Uv0gw0vy0Yzhzz0_zT3zzAzz\ IztOzlWzdbzXhzQdzU_zXWz_QzbOze<2>Azo6zr3ztzzGwzJ\ <3>qzWvz_ozYhzYbzYPzMYzYGzjAzr5zy } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= Stellar_Nursery { ; 4-1/2min at 640x480 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-0.09294912167762445/+0.00143386807667\ 271/1.009587e+007/1/180 params=100/1/1/100/-0.99/0 float=y maxiter=1500 bailout=25 inside=0 logmap=90 symmetry=none periodicity=10 colors=000ADa0Cj2AmC9mA8om6qz0or8rgJtUUvFew5ry0zz\ 0zz1zy5ywAvvFrtFtzJotMlmPggUdaXaW__PbYL60AC8QGG_L\ PdddIgqI8_CDYIIXOMWUQU_WTeaIge8gl0gq0gj0a<2>U0JP0\ DJ08800F03L06Q09X0Cd2Fj5Iq9Lv3MwCOoJPgQQ_YTTeULmW\ FvXJrUOoTTlPXhOWoJ_gMd_OhTPlLQqDTv6Uy0Wo6XeDYYLYP\ T_I__9ga0tb2ma3ga6ba8XaAQaCMaFGaD6gGCa<2>OPJQWDT_\ 8Wd2Wg0Xh0Xh1Xj5Qo1Xj8aOFe2MgAThJY<3>otwtzzqzzowv\ lqojlhhebe_XdUQjUMbPL<2>JCGD8F83D21D9W0Ga0Y0gbC_e\ _ThyLazJWzJOzI<2>2zD0zC0zC0z92z88z6Dz3Jz2Pz1<4>vz\ 0zz0<2>yy0ht0Uo0Fj11e30a60Y9<2>0QI0OL2LO5IQ6GU9DX\ AA_<3>L1lD0rM0oW1l<2>w8bz8d<2>z9YwAWrCUoDTlFQhGOe\ IMaJLYLIWMGTOFLPFPQDTTCWUAYWAbX9eY8h_8la6ob5td3we\ 3zg2zh1zj3zl1zm0to0lq0<2>Uv0gw0vy0Yzhzz0_zT3zzAzz\ IztOzlWzdbzXhzQdzU_zXWz_QzbOze<2>Azo6zr3ztzzGwzJ\ <3>qzWvz_ozYhzYbzYPzMYzYGzjAzr5zy } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Wed May 5 01:33:34 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id AAA09451 for philofractal-list; Wed, 5 May 1999 00:33:30 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp0.mindspring.com (smtp0.mindspring.com [207.69.200.30]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id XAA09267; Tue, 4 May 1999 23:54:51 -0500 Received: from LOCALNAME (user-2iveijj.dialup.mindspring.com [165.247.74.115]) by smtp0.mindspring.com (8.8.5/8.8.5) with SMTP id AAA04053; Wed, 5 May 1999 00:53:55 -0400 (EDT) Date: Wed, 5 May 1999 00:53:55 -0400 (EDT) Message-Id: <1.5.4.16.19990505005301.2adff28e@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 05-05-99 (Wherever Minibrot) (c) Cc: fractal-art@icd.com Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- May 05, 1999 Fractal enthusiasts: The M-Mix4 formula did it again! With just a tiny bit of help from Photoshop 5.0, it produced today's fractal picture, which resembles nothing as much as another of those child's windmills. The contrast was increased about 25 percent in the graphics program, though the basic colors were created with nothing more than the 'E' screen of Fractint. (The 'E' screen appears in graphics mode. Fractint really needs its screens such as X, Y, Z, R, G, V, etc. converted to graphics mode also. [I realize it's a task.] I switch my monitors back and forth from text to graphic modes hundreds of times every fractal session. When the fractal fever strikes, I really have those monitor relays clicking. Fortunately, my monitors seem to be built like brick s---houses, but the switching delay does become annoying at times.) I named the picture "Wherever Minibrot". The name came to mind when I realized that the formula Z+1/Z+1.5C, which I was working with, just should not make a fractal. My thought was "wherever did that Minibrot come from?" The wherever image has been JPG'd and posted to: and to: I have been requested for comparison purposes to give the exact time the Fractal of the Day image takes to calculate. The time comment in the parameter files, accurate to 1/100 of a second, will indicate how long it took the parameter file to run on a PentiumMMX, 233MHZ in 640x480x256 mode. If anyone knows of a significantly faster processor, I would appreciate the information. I'd like to have some particular parameter file set aside as a benchmark for calculation time comparison purposes. This way we could determine which processors really are the fastest with Fractint, and with Ultra fractal as well. And now it's time to wrap up the fractals, shut down ye olde shoppe and settle by the TV for a few minutes rest and relax- ation. The weather today was variably cloudy with a tempera- ture of 75F 24C, and not a tornado in sight. Until next time, take care, and the fractals just keep getting better. Jim Muth jamth@mindspring.com START FORMULA============================================= MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END FORMULA=============================================== START PARAMETER FILE====================================== Wherever_Minibrot {;00:19:09.70 - Pentium 233mhz, SF5 reset=1960 type=formula formulafile=jim.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.58459853893407700/-0.00367547689805487\ /4.076451e+011/1/79.999 params=1/1/1/-1/0.5/0 float=y maxiter=4000 bailout=25 inside=0 logmap=427 symmetry=xaxis periodicity=10 colors=000Y2MY2M<7>YHYYIaYMbYNdYPf_RgaSd<2>b_VbbSdfP\ djMfmI<2>gv8gy4iz2gz2gz2fy2fx2dv2du2bs2br2ap2ao2_o2_\ m2Yl2Yj2Xi2Xg2Vf2Vd2Ub2Ua2Sa2S_2RY2RX2PV2PU2NS2NR2MP\ 2MN2KN2KM2IK2II2HH2HF2FD2FB2D92D82D82F91H91H91IB1KB1\ KB1MB1MD1ND1PD1PD1RF1RF1SF1UH1UH1VH1VH1XI1YI1YI1_I1a\ K1aK1bK1bM1dM1fM1fM1gN0gN0iN0jP0jP0lP0lP0mR0oR0oS0pS\ 0rS0rS0sS0sT0uT0vU0vU0xV0xV0yV0zV0zX0<5>zY0zZ1zY0<4>\ zV0zU0zU0zU0<5>zU0zT0zT0zS0zS0<11>yG0yF0yD0yB0yA0xA1\ vA2uA2sA4rA4pA6o98kA8hE9dI9aKBYNDaMDdNFbSFaXH__IYbIX\ fKVgKUjMUlMVmHXmBXm6Ym1Ym0_m0Yo0_o0_p0_p0_r0_r0as0as\ 0au0au0av0av0bx0<3>bz0bz0dz0<3>dz0dz0fz0<8>gz0gz0iz0\ <9>jz0jz0lz0<7>mz0VzBVz8Vz6Xz4Xz2Xz0Xz0Xz0 } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= Wherever_Minibrot {;00:19:09.70 - Pentium 233mhz, SF5 reset=1960 type=formula formulafile=jim.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.58459853893407700/-0.00367547689805487\ /4.076451e+011/1/79.999 params=1/1/1/-1/0.5/0 float=y maxiter=4000 bailout=25 inside=0 logmap=427 symmetry=xaxis periodicity=10 colors=000Y2MY2M<7>YHYYIaYMbYNdYPf_RgaSd<2>b_VbbSdfP\ djMfmI<2>gv8gy4iz2gz2gz2fy2fx2dv2du2bs2br2ap2ao2_o2_\ m2Yl2Yj2Xi2Xg2Vf2Vd2Ub2Ua2Sa2S_2RY2RX2PV2PU2NS2NR2MP\ 2MN2KN2KM2IK2II2HH2HF2FD2FB2D92D82D82F91H91H91IB1KB1\ KB1MB1MD1ND1PD1PD1RF1RF1SF1UH1UH1VH1VH1XI1YI1YI1_I1a\ K1aK1bK1bM1dM1fM1fM1gN0gN0iN0jP0jP0lP0lP0mR0oR0oS0pS\ 0rS0rS0sS0sT0uT0vU0vU0xV0xV0yV0zV0zX0<5>zY0zZ1zY0<4>\ zV0zU0zU0zU0<5>zU0zT0zT0zS0zS0<11>yG0yF0yD0yB0yA0xA1\ vA2uA2sA4rA4pA6o98kA8hE9dI9aKBYNDaMDdNFbSFaXH__IYbIX\ fKVgKUjMUlMVmHXmBXm6Ym1Ym0_m0Yo0_o0_p0_p0_r0_r0as0as\ 0au0au0av0av0bx0<3>bz0bz0dz0<3>dz0dz0fz0<8>gz0gz0iz0\ <9>jz0jz0lz0<7>mz0VzBVz8Vz6Xz4Xz2Xz0Xz0Xz0 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Thu May 6 01:33:34 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id AAA18314 for philofractal-list; Thu, 6 May 1999 00:33:43 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp1.mindspring.com (smtp1.mindspring.com [207.69.200.31]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id AAA18192; Thu, 6 May 1999 00:19:01 -0500 Received: from LOCALNAME (user-2ivehh9.dialup.mindspring.com [165.247.70.41]) by smtp1.mindspring.com (8.8.5/8.8.5) with SMTP id BAA15213; Thu, 6 May 1999 01:17:28 -0400 (EDT) Date: Thu, 6 May 1999 01:17:28 -0400 (EDT) Message-Id: <1.5.4.16.19990506011627.2adfd7fc@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 06-05-99 (A Sporadic Midget) (c) Cc: fractal-art@icd.com Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- May 06, 1999 Fractal enthusiasts: There are organized fractals, where the midgets can be found by a careful examination of the surrounding landscape. The midgets in these organized fractals have well-organized and rather predictable patterns around them. There are also disorganized fractals, where midgets appear in a random, haphazard manner. The midgets of these disorganized fractals appear almost without warning, and finding them is largely a matter of luck. Most of the midgets I feature in my FOTD's are of the organized variety. Today's midget, however, is of the disorganized kind. Organized midgets have the 2-4-8... series of features around the midget; today's midget is surrounded by random elements, which share a certain shape-theme, but have no organized 2-4-8... sequence. The overall effect is one of jagged shards of fractal debris swirling into a deep midget. To produce today's picture, I mixed various portions of Z^(-3) and Z^1.5, using the M-Mix4 formula, of course. I named the picture "A Sporadic Midget" because it appeared in a hit-or-miss manner where I was expecting nothing but chaos. I gave the image the usual slight boost in a graphics program. The JPEG file has been posted to: and to: where it awaits easy viewing. The weather was perfect today here at fractal central -- variably cloudy and humid, with a temperature of 75F 24C, and a spit of rain at sunset. I have sometimes seen it claimed that God is a fractal. It's an interesting thought, but a bit over-simplified. I would rather propose that God shares something of the mathematical nature of fractals. Of course, if this relation were considered true, it would mean that fractals have within them a rudimentary kind of consciousness, since God is ultimate consciousness. While watching the TV news coverage of the latest disaster earlier today, I saw someone wonder how God could do such a thing, or permit such a thing to happen. This is the ultimate theological question -- how can evil and injustice exist in a world ruled by an all-good, all-powerful, and all-knowing God. God must have these three attributes or He/She would not be the infinite God taught by our religions. This is one of those "it's a mystery, so sit down and shut up" questions I asked the nuns in eighth grade. The usual answer involves the so-called gift of free will. But this raises the question of why an all- knowing God would give free will to a race He/She knew was not yet mature enough to use it for the growth She/He intended. And it says nothing at all about natural disasters such as tornadoes and earthquakes, which appear to be aimed by God at certain unfortunate individuals, or else ignored altogether by God, who could stop them with only a passing thought. I've got lots more I could get into, but I see we're once again drifting from the topic, so I'd best shutter down the fractal shoppe for another night and flop into that overstuffed chair for a junky movie. Until tomorrow, when I'll be back with another fractal, take care, and see you then. Jim Muth jamth@mindspring.com START FORMULA============================================= MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END FORMULA=============================================== START PARAMETER FILE====================================== A_Sporadic_Midget {;0:10:04.84 at 233mhz, 640x480x256 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+8.95796361543905700/+2.12404476348569300\ /126.9947/1/157.499 params=0.3/-3/-0.3/1.5/0/1000 float=y maxiter=6000 bailout=25 inside=0 logmap=60 symmetry=none periodicity=10 colors=000z00<12>z00z00x00<2>w00w00u00u00s02<2>r02r0\ 2p02p02n02n04l04<2>k04k04i04i06g06g06g06e06e06d06d06\ b08b08b08_08_08Y08Y08Y08_0Ab0Ad0Ae0Cg4Ci6Ck8ElAEnCEp\ GGpIGrKGsMGuOIwRIxTIzVKzXKz_KzbMzdMzeMzgMzkO<2>zpPzr\ PzuPzwRzxRzzRzzOzzPzzRzzRzzTzzTzxVzwVzwXzuYzuYzs_zr_\ zrbzpbzpdzndzlezlgxkgwkiuiiugksgkrelpenndnlbpkbpk_ri\ _rgYseYsdXubVw_Vw_TxYTxXRzVPzTPzROzPOzPMzOKzMKzKIzII\ zGGzAEzCEzECzGCzIAzK8zM8zO6zQ6zS4zU2zW2zX0z<4>a0zb0z\ c2zd6ze8zfCzgGzhIziMzjPzkOzlIzmEznAz<3>r2zs0zt0z<2>w\ 0zx0zw0z<2>w0zw0zu0z<2>u0zu0zs0z<7>r0zr0zp0z<2>p0zp0\ zn0z<2>n0zn0zl0z<5>k0zeAzg8zg8zi6zk6zl4zn4zp2zr2zs0z\ u0zu0zw0zx0zz0z<27>z0z } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= A_Sporadic_Midget {;0:10:04.84 at 233mhz, 640x480x256 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+8.95796361543905700/+2.12404476348569300\ /126.9947/1/157.499 params=0.3/-3/-0.3/1.5/0/1000 float=y maxiter=6000 bailout=25 inside=0 logmap=60 symmetry=none periodicity=10 colors=000z00<12>z00z00x00<2>w00w00u00u00s02<2>r02r0\ 2p02p02n02n04l04<2>k04k04i04i06g06g06g06e06e06d06d06\ b08b08b08_08_08Y08Y08Y08_0Ab0Ad0Ae0Cg4Ci6Ck8ElAEnCEp\ GGpIGrKGsMGuOIwRIxTIzVKzXKz_KzbMzdMzeMzgMzkO<2>zpPzr\ PzuPzwRzxRzzRzzOzzPzzRzzRzzTzzTzxVzwVzwXzuYzuYzs_zr_\ zrbzpbzpdzndzlezlgxkgwkiuiiugksgkrelpenndnlbpkbpk_ri\ _rgYseYsdXubVw_Vw_TxYTxXRzVPzTPzROzPOzPMzOKzMKzKIzII\ zGGzAEzCEzECzGCzIAzK8zM8zO6zQ6zS4zU2zW2zX0z<4>a0zb0z\ c2zd6ze8zfCzgGzhIziMzjPzkOzlIzmEznAz<3>r2zs0zt0z<2>w\ 0zx0zw0z<2>w0zw0zu0z<2>u0zu0zs0z<7>r0zr0zp0z<2>p0zp0\ zn0z<2>n0zn0zl0z<5>k0zeAzg8zg8zi6zk6zl4zn4zp2zr2zs0z\ u0zu0zw0zx0zz0z<27>z0z } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Fri May 7 00:33:35 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id XAA27030 for philofractal-list; Thu, 6 May 1999 23:33:39 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp4.mindspring.com (smtp4.mindspring.com [207.69.200.64]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id XAA27014; Thu, 6 May 1999 23:32:51 -0500 Received: from LOCALNAME (user-2ivegh6.dialup.mindspring.com [165.247.66.38]) by smtp4.mindspring.com (8.8.5/8.8.5) with SMTP id AAA16578; Fri, 7 May 1999 00:31:12 -0400 (EDT) Date: Fri, 7 May 1999 00:31:12 -0400 (EDT) Message-Id: <1.5.4.16.19990507003004.2ae72444@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 07-05-99 (Baubled Mandelbrot) (c) Cc: fractal-art@icd.com Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- May 07, 1999 Fractal enthusiasts: Sometimes while I am working with fractals, a great sleepiness comes over me. (Some say it shows.) At these times, the monitor screen begins to appear snowy, looking almost like a TV set receiving a weak signal. When I see the snow on the screen, my memory seems to open up to vague, barely remembered dream scenes, locations and situations that I find myself in in my dreams. Curiously enough, when fully awake I cannot recall these scenes. It is only when I am in danger of dozing off that I have a half- way clear memory of these fantastic locations. At times like the present, when I am fully awake, I have only the vaguest memory of them. But it is enough of a memory to let me know that there is much which I cannot recall. There are about six major scenarios, potential dreams that start brewing as I doze off. And by noting which scene appears while I am falling asleep, I can often foretell the nature of the dreams to follow. Occasionally, I seem to drift directly from remembering the scene to the scene itself, without benefit of falling asleep. But I must fall asleep, because sometimes such vivid dreams end with an awakening. I mention dreams because in one of my dream scenarios, fractals are real objects, which exist in a seemingly outer objective world. These three-dimensional things appear hovering in mid- air or lying inconspicuously on the ground. It's too bad that fractals are 'real' only in an 'unreal' world. Today's fractal is real enough, as long as one considers the image projected onto a monitor screen to be real. I named the picture "Baubled Mandelbrot" because of the collection of shiny baubles surrounding the central Mandel-midget. The parameter file runs in 3 minutes, but it can be obtained in slightly less time by downloading it from: or from: To create the fractal, I broke out the M-Mix4 formula, subtrac- ted Z^(-11.1) from Z^11 and added 0.1C. The parameters are totally whimsical, done with no outcome intended, nor any idea of what would result. The weather today here at Fractal Central was quite unpleasant for anything but fractals, for which it was perfect. Low clouds, occasional drizzle, raw east winds and a temperature of 62F 16.5C made the fractal seeking perfect. And now, I'm perfectly ready to settle into my TV chair and watch the dullest show I can find. Until tomorrow, take cake, and the next time you see a live fractal, repeat "I do believe, I do believe...". Jim Muth jamth@mindspring.com START FORMULA============================================= MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END FORMULA=============================================== START PARAMETER FILE====================================== Baubled_Mandelbrot {; 0:03:19.96 on a p233, 640x480 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.99586940598452970/+0.08299760448780\ 566/48300.59/1/-150 params=1/11/-1/-11.1/-0.9/0 float=y maxiter=12000 bailout=25 inside=0 logmap=29 symmetry=none periodicity=10 colors=000a3`b2`<4>T1SR1RO1PL1NI1LF0K<3>4BD<13>Tp\ KVsKWuKYwL_yLazMbzM<2>gxN<20>HUc<7>9aE9bBAdE<12>C\ sh`mi<3>MJy<11>n5yp4yq6u<13>zU9<15>byO`zPZzQ<16>9\ zd<5>Xz`<3>XzZXzZZz`<3>ezh<4>Zzv<7>lzH<9>6zi<11>A\ zm<4>Tzz<4>7zv<6>uzh<3>yzL<11>gzkPzc<3>9zT<10>zzk\ <3>nzd } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= Baubled_Mandelbrot {; 0:03:19.96 on a p233, 640x480 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.99586940598452970/+0.08299760448780\ 566/48300.59/1/-150 params=1/11/-1/-11.1/-0.9/0 float=y maxiter=12000 bailout=25 inside=0 logmap=29 symmetry=none periodicity=10 colors=000a3`b2`<4>T1SR1RO1PL1NI1LF0K<3>4BD<13>Tp\ KVsKWuKYwL_yLazMbzM<2>gxN<20>HUc<7>9aE9bBAdE<12>C\ sh`mi<3>MJy<11>n5yp4yq6u<13>zU9<15>byO`zPZzQ<16>9\ zd<5>Xz`<3>XzZXzZZz`<3>ezh<4>Zzv<7>lzH<9>6zi<11>A\ zm<4>Tzz<4>7zv<6>uzh<3>yzL<11>gzkPzc<3>9zT<10>zzk\ <3>nzd } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Sat May 8 00:33:51 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id XAA02830 for philofractal-list; Fri, 7 May 1999 23:33:40 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp0.mindspring.com (smtp0.mindspring.com [207.69.200.30]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id XAA02705; Fri, 7 May 1999 23:19:42 -0500 Received: from LOCALNAME (user-2iveika.dialup.mindspring.com [165.247.74.138]) by smtp0.mindspring.com (8.8.5/8.8.5) with SMTP id AAA22765; Sat, 8 May 1999 00:17:40 -0400 (EDT) Date: Sat, 8 May 1999 00:17:40 -0400 (EDT) Message-Id: <1.5.4.16.19990508001627.2adf2e4a@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 08-05-99 (A Sea-Green Midget) (c) Cc: fractal-art@icd.com Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- May 08, 1999 Fractal enthusiasts: A peaceful image -- amber and green -- passes for today's Fractal of the Day. The scene was created by entering parameters at random into the M-Mix4 formula until something interesting resulted. The parameters of today's picture, totally whimsical, created a twisted, bubbly kind of M-set. A search of the East Valley area of this set found today's fractal. I have named the picture "A Sea-Green Midget". Actually, the picture has more amber than sea green, but the fractal foliage spreading from the tiny central midget has a pleasant turquoise hue, which inspired the name. The parameter file calculates in only a few minutes, but picking up the JPEG file from one of the sites where it is posted will produce a finished picture in even less time. Those sites are the Usenet group: and Paul's web site at: The weather today here at Fractal Central was a repeat of yester- day -- cloudy, drizzly, a temperature of 64F 18C -- most unpleasant for anything but seeking fractals. As today's image shows, I sought and found. That's it for tonight, fractal fans. Today's fractal might have been perfect, but even if it was, tomorrow's will be even better. Until then, take care, and when it drizzles, don't be a drizzle-puss -- find a fractal. Jim Muth jamth@mindspring.com START FORMULA============================================= MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END FORMULA=============================================== START PARAMETER FILE====================================== A_Sea-Green_Midget { ; time=0:07:03.97, p233, 640x480 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.2575596172981652/-0.8116578456060259/1\ .970597e+009/1/-117.499 params=1.1/1.1/-1.1/-1.1/0/0 float=y maxiter=1600 bailout=25 inside=0 logmap=156 symmetry=none periodicity=10 colors=000dL7<12>pXJqYKrZM<6>yeTzfUzeS<2>x_OwXNuVLsT\ K<7>OK8<2>1H4<25>nxm<11>hbzHtt<14>LvBLv8NqD<5>TPe\ <26>wrK<14>4Vu<6>l7R<7>gxD<23>Ptg<5>uU_<15>haggahfbh\ fci<8>_lmZmnYmnXmoXmo<11>kmm<3>QmW<10>ymN<4>wmR } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= A_Sea-Green_Midget { ; time=0:07:03.97, p233, 640x480 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.2575596172981652/-0.8116578456060259/1\ .970597e+009/1/-117.499 params=1.1/1.1/-1.1/-1.1/0/0 float=y maxiter=1600 bailout=25 inside=0 logmap=156 symmetry=none periodicity=10 colors=000dL7<12>pXJqYKrZM<6>yeTzfUzeS<2>x_OwXNuVLsT\ K<7>OK8<2>1H4<25>nxm<11>hbzHtt<14>LvBLv8NqD<5>TPe\ <26>wrK<14>4Vu<6>l7R<7>gxD<23>Ptg<5>uU_<15>haggahfbh\ fci<8>_lmZmnYmnXmoXmo<11>kmm<3>QmW<10>ymN<4>wmR } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Sun May 9 02:23:53 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id BAA12216 for philofractal-list; Sun, 9 May 1999 01:24:30 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp5.mindspring.com (smtp5.mindspring.com [207.69.200.82]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id BAA12061; Sun, 9 May 1999 01:16:04 -0500 Received: from LOCALNAME (user-2iveipk.dialup.mindspring.com [165.247.75.52]) by smtp5.mindspring.com (8.8.5/8.8.5) with SMTP id CAA29210; Sun, 9 May 1999 02:13:42 -0400 (EDT) Date: Sun, 9 May 1999 02:13:42 -0400 (EDT) Message-Id: <1.5.4.16.19990509021222.295f339a@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 09-05-99 (Strings of Pearls) (c) Cc: fractal-art@icd.com Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- May 09, 1999 Fractal visionaries and enthusiasts: It's the day we honor our mothers here in the USA. And what better gift for mother than a string of pearls. Strings of pearls can be costly, but today's fractal is full of them, free for the taking, the only cost being the inordinate length of time required to draw the image from the parameter file. But even this cost can be discounted 95 percent by downloading the complete GIF file from: or from: Today's fractal has been posted in GIF format because JPEG causes an unacceptable degradation of the image. I named the picture "Strings of Pearls" after the pearl-like strings of fractal stuff surrounding the ever-present Minibrot. The parent fractal results from a combination of Z and Z^(-0.1) -- an unlikely mixture if ever there was one. I found the combination without thinking, (the turned-off brain shows), and entering values at random. The fractal is one of those chaotic ones, with no obvious 2,4,8,16... series of elements converging on the midget. These chaotic areas, (sandy areas I call them), are generally quite slow to calculate, and often not worth the effort. But the pearls in today's image make it worth the effort. A while back, someone commented that my fractals are old- fashioned. Quaint is the word they used. Actually, in the world of fractals, old-fashioned means ten years ago. In a way, I'm still back there in the early days, when there was only one fractal -- the Mandelbrot set -- and every day someone discovered something fascinatingly new in some as yet unexplored area of that universal fractal. Today, the M-set has been pretty well explored -- at least to the depths to which it is convenient to dive. And we pretty well know what lies in any given part of the set before we actually see it. (Though the details make it still worth the effort.) It is only when two or more powers of Z are combined that totally new and unexpected things appear, which is why I use the M-Mix4 formula so often. I'll probably use the same formula again tomorrow, when there is always that ever-present chance that I'll start philosophizing. So until then, when the truth will be known, take care, and eat, drink and sleep fractals. Jim Muth jamth@mindspring.com START FORMULA============================================= MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END FORMULA=============================================== START PARAMETER FILE====================================== Strings_of_Pearls { ; 0:57:35.65 p233 640x480 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-1.012579120942516/+0.1447176688745201\ /47550.3 params=1/1/1/-0.1/0/0 float=y maxiter=40000 bailout=25 inside=0 logmap=223 symmetry=xaxis periodicity=10 colors=000HAA<4>LAAMAANABOAC<5>UAIUAIVAH<7>_AD_AC\ ZAC<3>YAANB9<3>MG7MH7LI8<2>LM8LN8LP9LR9LT9LV9LX9\ <9>LVBKVBKUCKTC<2>KRCKQCKQDKQDKPDKOD<12>JKGJKGJ\ KGJKGJJGJIG<6>JBIJAIJAIJAIJDI<2>NNHPQHQSH<11>dpGe\ rGewF<34>i8Wi7Wi5V<51>i9ai9aj8`<3>gCdfDdfDeeEedFf\ <4>cJhcKicKicKj<5>cKmcKmcKmcKmcKm<21>cKm } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= Strings_of_Pearls { ; 0:57:35.65 p233 640x480 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-1.012579120942516/+0.1447176688745201\ /47550.3 params=1/1/1/-0.1/0/0 float=y maxiter=40000 bailout=25 inside=0 logmap=223 symmetry=xaxis periodicity=10 colors=000HAA<4>LAAMAANABOAC<5>UAIUAIVAH<7>_AD_AC\ ZAC<3>YAANB9<3>MG7MH7LI8<2>LM8LN8LP9LR9LT9LV9LX9\ <9>LVBKVBKUCKTC<2>KRCKQCKQDKQDKPDKOD<12>JKGJKGJ\ KGJKGJJGJIG<6>JBIJAIJAIJAIJDI<2>NNHPQHQSH<11>dpGe\ rGewF<34>i8Wi7Wi5V<51>i9ai9aj8`<3>gCdfDdfDeeEedFf\ <4>cJhcKicKicKj<5>cKmcKmcKmcKmcKm<21>cKm } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Mon May 10 02:24:25 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id BAA21593 for philofractal-list; Mon, 10 May 1999 01:23:49 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp4.mindspring.com (smtp4.mindspring.com [207.69.200.64]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id AAA21347; Mon, 10 May 1999 00:34:21 -0500 Received: from LOCALNAME (user-2iveiou.dialup.mindspring.com [165.247.75.30]) by smtp4.mindspring.com (8.8.5/8.8.5) with SMTP id BAA23382; Mon, 10 May 1999 01:31:36 -0400 (EDT) Date: Mon, 10 May 1999 01:31:36 -0400 (EDT) Message-Id: <1.5.4.16.19990510013009.2adfe6f8@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 10-05-99 (Pattern Number One) (c) Cc: fractal-art@icd.com Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- May 10, 1999 Fractal enthusiasts: Today I did what I swore I would never do. I got into a flame war on one of the political forums. (That's where the real wars are.) And I got myself so worked up that I almost forgot the FOTD. But in the nick of time, I remembered. Another trip to the M-Mix4 formula yielded today's fractal, which is a fractal but hardly looks like one. Still, the big flat clunky areas of solid color somehow blend together to form a recognizable pattern of the kind that surrounds a Minibrot. The midget itself lies at the center of the image, but alas, it is beyond reach. One can look and realize that the midget is there, only to be rebuffed in all efforts to access the little fellow. The fractal is what happens when a little bit of Z^3 ia added to a lot of Z^(-11), and the X-axis carefully examined. The color section of the parameter file is quite long. This is because I used a random palette for the picture. The image was not post-processed in a graphics program. The parameter file runs in anywhere from one minute to 34 minutes, depending on your processor. The JPEG file has been posted to: and to: The weather here today was perfect for mothers as well as fractals. A blue sky, warm sun, temperature of 77F 25C, and just enough wind to keep the kites aloft was perfect for anything. And now it's the end of another day as well as another FOTD. Nothing left for me to do but settle into my softest chair and watch some cartoons. I think I'll make it Danger Mouse tonight. In 23 hours and 17 minutes, I'll have another great, (IMO), fractal. Until then, take care, but don't take too much care. Jim Muth jamth@mindspring.com START FORMULA============================================= MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END FORMULA=============================================== START PARAMETER FILE====================================== Pattern_Number_One { ; 0:01:57.87 p233 640x480 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.96112362560552/0/1.779056e+012/0.999\ 9 params=0.007/3/11/-11/0/0 float=y maxiter=250 bailout=25 inside=0 logmap=88 symmetry=xaxis periodicity=0 colors=000R00c6EaDK_JPDxj_CYZGXZJWYM\ VVilZ7NbSV_TWZSVZRVYQUZzhYg`2F709vCFlNKbzIRpLSfNTj\ kXecWaWVH8WMX2QUCURLRvc0wmCpBpJqiLicNadcusojkfddYZ\ 0I1HMGhklzohYuu<2>YX`vDRE1RL9SSHTKQo`OyAY9IVGQSN__\ XZWWYSVqCRgJTxKeoMafOYfnE<2>_VQfWkcTe`R_wTvl`Uah2\ <3>LH4CV83hB27pACjIGdXORQLZZDgOg6S`EVVMx`PoXRfTTWq\ PXbSeH8yq8ogGfYNzXSpUTfRUzhaHJm<2>UOZAfTMYUOMT5q2\ <2>RWNBOzNPiLtzSdiEIPLLRSNTFvrPeeUeoWXdBR5NQILIwQL\ mUNcaSe<2>ZPXTnzZiVAVKITOQRRv8ImEMeKQTEiWKaJ8A<2>V\ LPeWE<2>_QQPNljbd<2>`SWCNAKOHRPO9teMd_`UBPCcUJZllZ\ BRqJQiRPaDAWKFVRKUABfIGaQLYEiCLbISWOQY39sX<2>SWUN4\ nTFcG3kMBeSI_XhVBAfNI_j6u0PRCPSNPT5lEFdKPXPy3woBmf\ IcNaf<2>WSXqYwLMz<2>VParSigQaSLOUNQWOSKoMPfPUYSDC7\ KHFRLNnVh<2>aQXIsp<2>UWZ0Xw<2>QR`6aN<2>RSTDukKjeR\ __62EGAKPIPND7khn<2>`UZnSkeQbwD1pG9jJG } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= Pattern_Number_One { ; 0:01:57.87 p233 640x480 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.96112362560552/0/1.779056e+012/0.999\ 9 params=0.007/3/11/-11/0/0 float=y maxiter=250 bailout=25 inside=0 logmap=88 symmetry=xaxis periodicity=0 colors=000R00c6EaDK_JPDxj_CYZGXZJWYM\ VVilZ7NbSV_TWZSVZRVYQUZzhYg`2F709vCFlNKbzIRpLSfNTj\ kXecWaWVH8WMX2QUCURLRvc0wmCpBpJqiLicNadcusojkfddYZ\ 0I1HMGhklzohYuu<2>YX`vDRE1RL9SSHTKQo`OyAY9IVGQSN__\ XZWWYSVqCRgJTxKeoMafOYfnE<2>_VQfWkcTe`R_wTvl`Uah2\ <3>LH4CV83hB27pACjIGdXORQLZZDgOg6S`EVVMx`PoXRfTTWq\ PXbSeH8yq8ogGfYNzXSpUTfRUzhaHJm<2>UOZAfTMYUOMT5q2\ <2>RWNBOzNPiLtzSdiEIPLLRSNTFvrPeeUeoWXdBR5NQILIwQL\ mUNcaSe<2>ZPXTnzZiVAVKITOQRRv8ImEMeKQTEiWKaJ8A<2>V\ LPeWE<2>_QQPNljbd<2>`SWCNAKOHRPO9teMd_`UBPCcUJZllZ\ BRqJQiRPaDAWKFVRKUABfIGaQLYEiCLbISWOQY39sX<2>SWUN4\ nTFcG3kMBeSI_XhVBAfNI_j6u0PRCPSNPT5lEFdKPXPy3woBmf\ IcNaf<2>WSXqYwLMz<2>VParSigQaSLOUNQWOSKoMPfPUYSDC7\ KHFRLNnVh<2>aQXIsp<2>UWZ0Xw<2>QR`6aN<2>RSTDukKjeR\ __62EGAKPIPND7khn<2>`UZnSkeQbwD1pG9jJG } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Tue May 11 00:46:57 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id XAA30303 for philofractal-list; Mon, 10 May 1999 23:46:47 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp2.mindspring.com (smtp2.mindspring.com [207.69.200.32]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id XAA30166; Mon, 10 May 1999 23:16:53 -0500 Received: from LOCALNAME (user-2iveg0d.dialup.mindspring.com [165.247.64.13]) by smtp2.mindspring.com (8.8.5/8.8.5) with SMTP id AAA11289; Tue, 11 May 1999 00:14:00 -0400 (EDT) Date: Tue, 11 May 1999 00:14:00 -0400 (EDT) Message-Id: <1.5.4.16.19990511001227.29775cce@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 11-05-99 (Fractalled Lightning) (c) Cc: fractal-art@icd.com Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- May 11, 1999 Fractal enthusiasts: Today's fractal is a modest effort -- an image I conjured up in a hurry with the M-Mix4 formula. It's not the best I've ever done, but it has a certain kind of frantic celestial serenity about it that defies description. Therefore, instead of describing it, I'll let the picture speak fot itself. Actually, I lack the time to give a proper description. But by tomorrow I'll have my energies restored, and watch out world when the fractals start coming again. The picture is now speaking for itself at: and at: The weather today was the best in many months here at Fractal Central. The deep blue sky, light north winds, brilliant warm sun and temperature of 77F 25C were absolutely perfect for fractal searching. But as stated above, my search was short- circuited by other tasks. Tomorrow, however, is but 24 hours away, and I'll return then with a new fractal for sure and a 98 percent probability of some not altogether optimistic philosophy. Until then, take care and have you tried the new line of diet fractals? (:-P) Jim Muth jamth@mindspring.com START FORMULA============================================= MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END FORMULA=============================================== START PARAMETER FILE====================================== FractaledLightning { ; 0:07:53.63 p233 640x480 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-3.84515393892672/+5.426904801372345/3.0\ 27559e+009/1/10 params=-1/0.85/1/-0.85/0.9/1000 float=y maxiter=1500 bailout=25 inside=0 logmap=171 symmetry=none periodicity=10 colors=000A6A<5>A8AA82A8A<10>A9WA9YB9_C9aC9cE9e<2>A\ 9k89n79p59s49u29x19z<2>48i44c<30>CygCzgBgk6Mr<6>``R\ dcNigJmkFuqB<7>heBfdBedB<2>`bBZaBY_B<4>QTBORBOQ2NSB\ NYKMdTMjaOpm<25>5jM4jL1iL<10>UpJXqJ`rJ<5>uuJ<2>rtLu\ tLntLmsMjsMgsNfsNcsNbrOZrOXrP<4>KqRIqRHqR<5>7oU<2>D\ oVFoVHoU<18>roGtoFuoEvoE<6>zo9<16>zsXzsYztY<18>zmc } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= FractaledLightning { ; 0:07:53.63 p233 640x480 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-3.84515393892672/+5.426904801372345/3.0\ 27559e+009/1/10 params=-1/0.85/1/-0.85/0.9/1000 float=y maxiter=1500 bailout=25 inside=0 logmap=171 symmetry=none periodicity=10 colors=000A6A<5>A8AA82A8A<10>A9WA9YB9_C9aC9cE9e<2>A\ 9k89n79p59s49u29x19z<2>48i44c<30>CygCzgBgk6Mr<6>``R\ dcNigJmkFuqB<7>heBfdBedB<2>`bBZaBY_B<4>QTBORBOQ2NSB\ NYKMdTMjaOpm<25>5jM4jL1iL<10>UpJXqJ`rJ<5>uuJ<2>rtLu\ tLntLmsMjsMgsNfsNcsNbrOZrOXrP<4>KqRIqRHqR<5>7oU<2>D\ oVFoVHoU<18>roGtoFuoEvoE<6>zo9<16>zsXzsYztY<18>zmc } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Tue May 11 01:46:43 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id AAA30624 for philofractal-list; Tue, 11 May 1999 00:46:45 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from bo.nznet.gen.nz (ns1.nznet.gen.nz [203.167.232.34]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id XAA30377 for ; Mon, 10 May 1999 23:57:31 -0500 Received: from packrat.nznet.gen.nz (ms2-10.nznet.gen.nz [203.167.232.140]) by bo.nznet.gen.nz (8.8.7/8.8.8) with SMTP id QAA10485 for ; Tue, 11 May 1999 16:58:58 +1200 Message-Id: <3.0.3.32.19990511165230.006d873c@mail.nznet.gen.nz> X-Sender: packrat@mail.nznet.gen.nz X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.3 (32) Date: Tue, 11 May 1999 16:52:30 +1200 To: philofractal@icd.com From: "Morgan L. Owens" Subject: [philofractal] Whence simplicity? Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com Okay, so we have a pretty fair idea of where the intricate structure of the world comes from, despite relatively (and suspiciously) simple rules. But where does its simplicity come from? For a start, the rules are - as I said - suspiciously simple. The Navier-Stokes equations which underlie the movement of fluids (even unto turbulence) are only second-order differential equations. Why not third-order? Fourth? Higher? The Standard Model of quantum mechanics is pretty simple, too. More complex than seems strictly necessary perhaps, but still: six types of quark, six types of lepton, and four forces with their carrying particles (photons for electromagnetism, W and Z bosons for the weak force, gluons for the strong, and gravitons carrying gravitation). Much simpler than what _could_ be imagined ... the chemical elements could have been fundamental particles. All hundred-odd and counting of them. I look out of my window right now. My laundry is out there on the line. Pegs, bucket, fence, grass, tree (as Harry Enfield's aliens have it: _TREEE!_), garage, vege garden (not much at this time of year), clouds, ornaments. I could go on, but the fact is that sooner than I expect I'd run out of things to identify. Why are there so few? If I had botanical or horticultural experience I'd probably identify the plants that make up my lawn (I do recognise bits of paspallum, one or two daisies, patches of clover, the cursed Onehunga weed that I was sure I'd gotten rid of _last_ year...at least it's harmless 'til summer). But of all the astronomical things that _could_ be growing in my lawn, why do I see fewer than a dozen? Of all the uncountably many _possibilities_ available to the Universe, why is it so parsimonious? And given all the conceivable ways in which the Universe could be a lot more complex than it is (and there are of course a lot more ways in which it can be more complex than there are in which it can be simpler), why isn't it? Nature appears to strive for simplicity, according to scientific convention. Why? What's simplicity really got going for it, apart from making it easier for scientists? Well, I gotta go; there's some weeds that I need to get rid of... Morgan "The most incomprehensible thing about the universe is that it is comprehensible." Albert Einstein _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Tue May 11 10:50:22 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id JAA00935 for philofractal-list; Tue, 11 May 1999 09:46:29 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp1.mindspring.com (smtp1.mindspring.com [207.69.200.31]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id JAA00868 for ; Tue, 11 May 1999 09:31:24 -0500 Received: from default (user-38ldgv4.dialup.mindspring.com [209.86.195.228]) by smtp1.mindspring.com (8.8.5/8.8.5) with SMTP id KAA04468 for ; Tue, 11 May 1999 10:28:25 -0400 (EDT) From: "Jason Hine" To: Subject: Re: [philofractal] Whence simplicity? Date: Tue, 11 May 1999 07:27:39 -0700 Message-ID: <01be9bba$6c19b900$e4c356d1@default> MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 4.71.1712.3 X-MimeOLE: Produced By Microsoft MimeOLE V4.71.1712.3 Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com MLO wrote: >Okay, so we have a pretty fair idea of where the intricate structure of the >world comes from, despite relatively (and suspiciously) simple rules. But >where does its simplicity come from? Well, we have a pretty fair idea of where the intricate structure of the Mandelbrot Set comes from, despite relatively (and suspiciously) simple rules. But where does its simplicity come from? (apologies to MLO) >For a start, the rules are - as I said - suspiciously simple. The >Navier-Stokes equations which underlie the movement of fluids (even unto >turbulence) are only second-order differential equations. Why not >third-order? Fourth? Higher? The movements of a homogenous fluid are the interactions of a single type of pattern; there is one set of characteristics to describe how the molecules of the fluid interact with each other. Can I generalize this and say: physical interactions between large numbers of similar objects can be described well by second-order differential equations? Water molecules, Jell-o, a crowd at a demonstration (to a point... there's always those phase-transitions to watch out for)... [snip] >I look out of my window right now. My laundry is out there on the line. >Pegs, bucket, fence, grass, tree (as Harry Enfield's aliens have it: >_TREEE!_), garage, vege garden (not much at this time of year), clouds, >ornaments. I could go on, but the fact is that sooner than I expect I'd run >out of things to identify. Why are there so few? Why are there only a limited number of basic patterns observable around the edge of the Mandelbrot set? >If I had botanical or horticultural experience I'd probably identify the >plants that make up my lawn (I do recognise bits of paspallum, one or two >daisies, patches of clover, the cursed Onehunga weed that I was sure I'd >gotten rid of _last_ year...at least it's harmless 'til summer). But of all >the astronomical things that _could_ be growing in my lawn, why do I see >fewer than a dozen? Why are fairly similar patterns found close to each other in the Mandelbrot set? >Of all the uncountably many _possibilities_ available to the Universe, why >is it so parsimonious? And given all the conceivable ways in which the >Universe could be a lot more complex than it is (and there are of course a >lot more ways in which it can be more complex than there are in which it >can be simpler), why isn't it? > >Nature appears to strive for simplicity, according to scientific >convention. Why? What's simplicity really got going for it, apart from >making it easier for scientists? I am not sure what you mean by "Nature appears to strive for simplicity, according to scientific convention." Life is not simplicity - you and I exist because *something* about this universe loves organized complexity. Call it God, call it a Principle of Organized Complexity... it's there. The Second Law of Thermodynamics needs revision, as does the Theory of Evolution (as do most (all?) human theories, I guess... ;-) Jason "Post-It Flipbook" Hine _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Tue May 11 13:53:05 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id MAA02313 for philofractal-list; Tue, 11 May 1999 12:48:37 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp3.mindspring.com (smtp3.mindspring.com [207.69.200.33]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id MAA02126 for ; Tue, 11 May 1999 12:33:21 -0500 Received: from LOCALNAME (user-2ivei5t.dialup.mindspring.com [165.247.72.189]) by smtp3.mindspring.com (8.8.5/8.8.5) with SMTP id NAA01279 for ; Tue, 11 May 1999 13:30:04 -0400 (EDT) Date: Tue, 11 May 1999 13:30:04 -0400 (EDT) Message-Id: <1.5.4.16.19990511133057.3347934a@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] Re: Whence simplicity Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com Morgan Owens wrote: >Okay, so we have a pretty fair idea of where the intricate >structure of the world comes from, despite relatively (and >suspiciously) simple rules. But where does its simplicity come >from? Perhaps we give ourselves a bit too much credit when it comes to understanding the universe. Perhaps the apparent simplicity is actually a reflection of the limits of human cognitive ability. If the various life forms of which we are aware were to be arranged on an ascending scale, we would find that man is the first and only species, (with the possible exception of apes and cetaceans), to have developed concepts such as self and universe. But man has a tendency to make himself into a god, forgetting that he is only the first species to develop these concepts. The lower animals do not waste time pondering things such as the self and the world; they have no concept of such things. Why then, do we assume that man, the most primitive species in our knowledge to have developed the concepts of self and universe, has developed the ultimately correct concept? Would not a far greater intelligence have developed a far different concept of reality? My answer to the simplicity question would be that the universe which we observe has been semi-intentionally simplified down to a level that we can mentally manipulate with with our faculty of reason. This attempt to simplify is perhaps nowhere more evident than in the field of quantum mechanics. QM is an embarrassment to rationalists. QM is so puzzling because we have not yet developed a model simple enough to make common- sense. The great rational scientists such as Asimov and Sagan almost totally avoided QM in their books. They did so because it troubled them that they could not reduce QM to a level where the laws of reason and common-sense could be applied to it. I see QM as the most glaring evidence that the ultimate truth, (if such a thing exists), lies beyond the scope of human reason. >For a start, the rules are - as I said - suspiciously simple. >The Navier-Stokes equations which underlie the movement of >fluids (even unto turbulence) are only second-order >differential equations. Why not third-order? Fourth? Higher? I think the rate of the nuclear reactions in the sun's interior is described by equations of something like the seventeenth order. (I could be wrong.) >Nature appears to strive for simplicity, according to >scientific convention. Why? What's simplicity really got going >for it, apart from making it easier for scientists? IMO, the simplicity is not merely making it easier for the scientists; the simplicity has been created *by* the scientists so that they may apply their faculty of reason to it. The Mandelbrot set is both a formula as simple as Z^2+C and an abstract object as complex as infinity, but we don't try to totally understand the infinite details -- we study the formula. It might be very similar with the universe, which just *might* be the world's greatest fractal. More with the FOTD in 12 hours. Jim Muth jamth@mindspring.com _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Tue May 11 23:50:32 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id WAA06062 for philofractal-list; Tue, 11 May 1999 22:46:35 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from bo.nznet.gen.nz (ns1.nznet.gen.nz [203.167.232.34]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id VAA05761 for ; Tue, 11 May 1999 21:57:00 -0500 Received: from packrat.nznet.gen.nz (ms2-05.nznet.gen.nz [203.167.232.135]) by bo.nznet.gen.nz (8.8.7/8.8.8) with SMTP id OAA20268 for ; Wed, 12 May 1999 14:58:12 +1200 Message-Id: <3.0.3.32.19990512145313.006fd364@mail.nznet.gen.nz> X-Sender: packrat@mail.nznet.gen.nz X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.3 (32) Date: Wed, 12 May 1999 14:53:13 +1200 To: philofractal@icd.com From: "Morgan L. Owens" Subject: Re: [philofractal] Re: Whence simplicity In-Reply-To: <1.5.4.16.19990511133057.3347934a@pop.mindspring.com> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com At 13:30 11/05/99 -0400, Jim Muth wrote: > QM is an >embarrassment to rationalists. QM is so puzzling because we >have not yet developed a model simple enough to make common- >sense. > That's because common sense evolved to help us find our next meal and keep us away from that sabre-tooth in the long grass. QM is only puzzling if you insist on a commonsense explanation. > The great rational scientists such as Asimov and Sagan >almost totally avoided QM in their books. They did so because >it troubled them that they could not reduce QM to a level where >the laws of reason and common-sense could be applied to it. > Remember that three hundred years ago electricity was a deeply puzzling phenomenon which, apart from such unmanageable things as lightning bolts, didnae occur in nature. It was just plain weird. Electricity was even more mysterious then than the strong nuclear force is now. Richard Feynman - another of those "great rational scientists" and arguably the smartest of the lot - and George Gamow - with his "Mr. Tompkins" stories - _did_ write about QM for the popular (though reasonably well-educated) market _The Feynman Lectures on Physics_ being a classic (even though it was intended for University undergraduates), with books being published today that consist pretty much entirely of extracts from the _Lectures_. And as for "reason" - if one could not reason about QM, one could not use computers to design microprocessors. :-) >>Nature appears to strive for simplicity, according to >>scientific convention. Why? What's simplicity really got going >>for it, apart from making it easier for scientists? > >IMO, the simplicity is not merely making it easier for the >scientists; the simplicity has been created *by* the scientists >so that they may apply their faculty of reason to it. The >Mandelbrot set is both a formula as simple as Z^2+C and an >abstract object as complex as infinity, but we don't try to > "Complex" or just "complicated"? An infinitely complex object would require an infinite amount of information to specify... An "ultimate truth" about QM will still need to accommodate the Standard Model (6 quarks, 6 leptons, 12 force-carrying particles mediating three forces) even after it's been extended to cover gravity; and it will have to explain why the nineteen parameters of the Model (the masses of the particles, the relative strengths of the forces etc.) have the values they do. In other words it would still have to _look_ like the Standard Model at Standard Model scales in the same way that relativistic dynamics looks like Newtonian mechanics at Newtonian scales (lim c->inf Einstein = Newton). And that is my question. If "ultimate reality" is supposed to be so darned weird, why can we so reliably get away with such simple models? Morgan L. Owens _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Wed May 12 00:50:05 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id XAA06317 for philofractal-list; Tue, 11 May 1999 23:46:37 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp0.mindspring.com (smtp0.mindspring.com [207.69.200.30]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id XAA06289; Tue, 11 May 1999 23:41:48 -0500 Received: from LOCALNAME (user-2ivein5.dialup.mindspring.com [165.247.74.229]) by smtp0.mindspring.com (8.8.5/8.8.5) with SMTP id AAA23991; Wed, 12 May 1999 00:38:34 -0400 (EDT) Date: Wed, 12 May 1999 00:38:34 -0400 (EDT) Message-Id: <1.5.4.16.19990512003654.2a87d990@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 12-05-99 (Quantum Uncertainty) (c) Cc: fractal-art@icd.com Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- May 12, 1999 Fractal enthusiasts and visionaries: I thrive on mysteries and uncertainties. And nothing is more uncertain than the goings-on in the quantum world. At that level, it is impossible to know at the same time both where a particle is located and what the particle is doing. And this uncertainty is not due to lack of sensitivity of our instru- ments. It exists because the attribute we are trying to measure has no well-defined value. I named today's fractal image "Quantum Uncertainty" because I'm not certain where it came from. I made it with the MandNewt05 formula, one of a series of formulas the purpose of which I have long since forgotten. But regardless of what these formulas were originally intended for, they do make interesting fractals. Today's picture is an indescribable mixture of balls and vaguely familiar surreal shapes. Most of it is bof60 inside fill. Studying the image, I get the impression of mighty forces at work, but hiding the work they are doing. The color is not as good as it could be, since I had only limited time to work on it. The attached Fractint parameter file runs in well under an hour on even the slowest 486. But if that is too slow, the GIF file has been posted in its incorrupted glory to: and to the Paul Lee's web site at: I posted today's image in GIF format because when I JPG'ed it, there was too much degradation. JPEG just doesn't work well with banded fractals. Tomorrow is another day. I'll be here then with another fractal and a good chance of a modicum of philosophy. The weather today was a perfect 77F 25C, with bright sun and light winds. Until next time, take care, and some things are best left unspoken. Jim Muth jamth@mindspring.com START FORMULA============================================= MandNewt05 {; Jim Muth z=c=fn1(pixel): a=z^2+(c-p1)*z-c b=p2*z^2+c-1 z=z-1*a/b p3 <= |a| } END FORMULA=============================================== START PARAMETER FILE====================================== QuantumUncertainty { ; 0:02:46.42 p233 640x480 reset=1960 type=formula formulafile=mandnewt.frm formulaname=MandNewt05 function=atanh passes=1 center-mag=0.194662/0.834647/0.2684708/1/35 params=-0.068/-2.935/2.424/-4.9/-0.265/-3.731 float=y maxiter=180 bailout=25 inside=bof60 logmap=yes symmetry=none periodicity=10 colors=000zsQ<2>mqNhpMfoLenK<14>JUGISGGPFFMFDJFCGFC\ FDBezBdz<5>8cx8cx7cx7cx7cx6cx<6>3cw3cv1cu<12>LSsJRs\ MQsPPpSOk<2>`L`<5>YFSYERYFQ<13>Ta7Tb6QIGNHPI5W<14>u\ WvxUxwXwv_wubw<4>pcwocwncvmcu<10>bcnacn_cl<4>Vcd<9>\ KEQGBO<11>gKPiLPjANkLPYWQKfR2kN6nS9jX<4>RFsS7x<9>fR\ uhTukTy<10>VVIUWDUVF<17>UDkVBmUDl<21>E_WsRGuPEvODyI\ A<5>nkJ } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= QuantumUncertainty { ; 0:02:46.42 p233 640x480 reset=1960 type=formula formulafile=mandnewt.frm formulaname=MandNewt05 function=atanh passes=1 center-mag=0.194662/0.834647/0.2684708/1/35 params=-0.068/-2.935/2.424/-4.9/-0.265/-3.731 float=y maxiter=180 bailout=25 inside=bof60 logmap=yes symmetry=none periodicity=10 colors=000zsQ<2>mqNhpMfoLenK<14>JUGISGGPFFMFDJFCGFC\ FDBezBdz<5>8cx8cx7cx7cx7cx6cx<6>3cw3cv1cu<12>LSsJRs\ MQsPPpSOk<2>`L`<5>YFSYERYFQ<13>Ta7Tb6QIGNHPI5W<14>u\ WvxUxwXwv_wubw<4>pcwocwncvmcu<10>bcnacn_cl<4>Vcd<9>\ KEQGBO<11>gKPiLPjANkLPYWQKfR2kN6nS9jX<4>RFsS7x<9>fR\ uhTukTy<10>VVIUWDUVF<17>UDkVBmUDl<21>E_WsRGuPEvODyI\ A<5>nkJ } frm:MandNewt05 {; Jim Muth z=c=fn1(pixel): a=z^2+(c-p1)*z-c b=p2*z^2+c-1 z=z-1*a/b p3 <= |a| } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Wed May 12 01:50:03 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id AAA06619 for philofractal-list; Wed, 12 May 1999 00:46:32 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp0.mindspring.com (smtp0.mindspring.com [207.69.200.30]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id AAA06563 for ; Wed, 12 May 1999 00:39:51 -0500 Received: from LOCALNAME (user-2ivei3t.dialup.mindspring.com [165.247.72.125]) by smtp0.mindspring.com (8.8.5/8.8.5) with SMTP id BAA03908 for ; Wed, 12 May 1999 01:36:37 -0400 (EDT) Date: Wed, 12 May 1999 01:36:37 -0400 (EDT) Message-Id: <1.5.4.16.19990512013457.296f378a@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] Re: Whence simplicity Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com At 02:53 PM 5/12/99 +1200, you wrote: >That's because common sense evolved to help us find our next >meal and keep us away from that sabre-tooth in the long grass. >QM is only puzzling if you insist on a commonsense explanation. True. But this apparent need to perceive the world in a common- sense way would seem to indicate that we shall never truly understand a theory of everything even if we do find one. What a disappointment if we do find the ultimate theory and it turns out that only the mathematical elite can understand it because it fills a book like the proof of the 4-color-map conjecture. >Remember that three hundred years ago electricity was a deeply >puzzling phenomenon which, apart from such unmanageable things >as lightning bolts, didnae occur in nature. It was just plain >weird. Electricity was even more mysterious then than the strong >nuclear force is now. Actually, electricity is still pretty mysterious. >Richard Feynman - another of those "great rational scientists" >and arguably the smartest of the lot - and George Gamow - with >his "Mr. Tompkins" stories - _did_ write about QM... And great books they are! >In other words it [the theory of everything] would still have >to _look_ like the Standard Model at Standard Model scales in >the same way that relativistic dynamics looks like Newtonian >mechanics at Newtonian scales (lim c->inf Einstein = Newton). > >And that is my question. If "ultimate reality" is supposed to >be so darned weird, why can we so reliably get away with such >simple models? I would hazard a guess that just as with Newtonian physics, the simple models are not exactly correct, but that the difference is so small as to be unnoticeable. Of course, when the uncertainty principle is taken into account, the departure may have no significance. Actually, this is one of those things that I really have no answer to. I must think about it for a while. Maybe an answer will pop into my head while I'm cooking a fractal. Jim M. _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Thu May 13 02:50:07 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id BAA16748 for philofractal-list; Thu, 13 May 1999 01:46:29 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp3.mindspring.com (smtp3.mindspring.com [207.69.200.33]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id AAA16429; Thu, 13 May 1999 00:58:22 -0500 Received: from LOCALNAME (user-2iveifd.dialup.mindspring.com [165.247.73.237]) by smtp3.mindspring.com (8.8.5/8.8.5) with SMTP id BAA01180; Thu, 13 May 1999 01:54:43 -0400 (EDT) Date: Thu, 13 May 1999 01:54:43 -0400 (EDT) Message-Id: <1.5.4.16.19990513015256.2adfb3b8@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 13-05-99 (Heart Land) (c) Cc: fractal-art@icd.com Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- May 13, 1999 Fractal visionaries and enthusiasts: The "Fractal of the Day" is in its 26th month and showing no signs of slowing down. (Though I have been told several times over that period that the worthless thing should dry up and blow away.) We've had a few too many Minibrots recently, so today's out-of- the-ordinary picture is a return to the MandNewt05 formula. This formula, as well as the other eleven MandNewt formulas, draws very interesting images when the inside fill is set to bof60. Today's picture is one of these images. I have named the picture "Heart Land" after the dark heart- shaped object toward the upper right. The scene features twisting lines of greenish spherical objects, which for some reason I call buckyballs. The overall impression is a surreal one, with hints of great things happening invisibly just beneath the surface. The parameter file runs in but a few minutes. The picture file has been posted in JPEG format to Usenet at: and to the WWW at: The Fractal Central weather today was warm and muggy, the most summer-like day so far this spring. The temperature of 86F 30C and light winds were perfect for lying around, searching for fractals. I searched, but I had no time to lie. I've been thinking lately of the holy grail of science -- a theory of everything. What a disappointment it would be if, when we find the theory, it turns out to be incomprehensible to all but the few mathematical geniuses who can understand the math. Even today, quantum mechanics is perilously near this stage. We have the QM equations, and we know that they work. But we don't know why they work. We lack a sensible corresponding physical model. Indeed, we now know that a totally accurate physical model of an atom is impossible. There is an old short story titled "He Who Shrank". The story is about a man who begins shrinking and can't stop. He eventu- ally shrinks to sub-atomic size, and finds that our atoms are actually infinitesimal planetary systems, with some atom-planets inhabited by intelligent life. What would one find if they actually shrank to the size of an atomic nucleus? With eyes much smaller than the wave length of visible light, would vision be possible? If vision were poss- ible, what would an atomic nucleus look like? My own mental model of an atomic nucleus is of something like a frothy, boiling rasberry, though I realize that this has no basis in fact. Maybe nothing is there at all but energy, and since energy cannot be seen, maybe a shrinking person would find only a vast emptiness. More on this in the future. Right now, it's past post time, and the FOTD has yet to be posted. I'll show up at this same spot again tomorrow, with more fractal goodies and perhaps some semi- wisdom. Until then, take care, and endure... Jim Muth jamth@mindspring.com START FORMULA============================================= MandNewt05 {; Jim Muth z=c=fn1(pixel): a=z^2+(c-p1)*z-c b=p2*z^2+c-1 z=z-1*a/b p3 <= |a| } END FORMULA=============================================== START PARAMETER FILE====================================== Heart_Land { ; 0:02:46.31, p233, 640x480 reset=1960 type=formula formulafile=mandnewt.frm formulaname=MandNewt05 function=atanh passes=1 center-mag=-0.111051/0.0507666/1.268047/1/-15 params=0.9141/3.2639/-3.3039/-1.0621/-0.3534/3.0686 float=y maxiter=180 bailout=25 inside=bof60 logmap=yes symmetry=none periodicity=10 colors=000msJ<12>OfFNeFNdF<14>KQAKPAIO3HJ0fwv<4>awq\ `wq_wpZwpYwo<6>RwlQwlPvlOul<32>uYltZmvYl<17>dYhcYhb\ YgaYf`Xh_Xg<33>4X_<8>gTbkTbpTbtTbzUdyTcwTb<4>jR_hRZ\ gQYdQWcOT<3>XLIWLFUJESJDRIDPHCPF8YLQ<9>SIJeHI<16>WB\ 7VB6UC6<29>i66jA7kA8lA9<10>mAA } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= Heart_Land { ; 0:02:46.31, p233, 640x480 reset=1960 type=formula formulafile=mandnewt.frm formulaname=MandNewt05 function=atanh passes=1 center-mag=-0.111051/0.0507666/1.268047/1/-15 params=0.9141/3.2639/-3.3039/-1.0621/-0.3534/3.0686 float=y maxiter=180 bailout=25 inside=bof60 logmap=yes symmetry=none periodicity=10 colors=000msJ<12>OfFNeFNdF<14>KQAKPAIO3HJ0fwv<4>awq\ `wq_wpZwpYwo<6>RwlQwlPvlOul<32>uYltZmvYl<17>dYhcYhb\ YgaYf`Xh_Xg<33>4X_<8>gTbkTbpTbtTbzUdyTcwTb<4>jR_hRZ\ gQYdQWcOT<3>XLIWLFUJESJDRIDPHCPF8YLQ<9>SIJeHI<16>WB\ 7VB6UC6<29>i66jA7kA8lA9<10>mAA } frm:MandNewt05 {; Jim Muth z=c=fn1(pixel): a=z^2+(c-p1)*z-c b=p2*z^2+c-1 z=z-1*a/b p3 <= |a| } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Thu May 13 05:49:58 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id EAA17760 for philofractal-list; Thu, 13 May 1999 04:46:42 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from bo.nznet.gen.nz (ns1.nznet.gen.nz [203.167.232.34]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id EAA17738 for ; Thu, 13 May 1999 04:43:51 -0500 Received: from packrat.nznet.gen.nz (ms2-10.nznet.gen.nz [203.167.232.140]) by bo.nznet.gen.nz (8.8.7/8.8.8) with SMTP id VAA12766 for ; Thu, 13 May 1999 21:46:27 +1200 Message-Id: <3.0.3.32.19990513213906.006fa7d0@mail.nznet.gen.nz> X-Sender: packrat@mail.nznet.gen.nz X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.3 (32) Date: Thu, 13 May 1999 21:39:06 +1200 To: philofractal@icd.com From: "Morgan L. Owens" Subject: Re: [philofractal] FOTD 13-05-99 (Heart Land) (c) In-Reply-To: <1.5.4.16.19990513015256.2adfb3b8@pop.mindspring.com> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com At 01:54 13/05/99 -0400, Jim Muth wrote: > > Indeed, we now know that a totally accurate physical >model of an atom is impossible. > That's the Copenhagen interpretation - a complete cop-out in my opinion, and has lost a lot of ground among the community of physicists since its inception (partly because most don't bother with the problem). It is possible to have a physically real universe in defiance of the Copenhagenists' claims. The problem is that it then becomes necessary to allow nonlocal interactions between events. Imagine a particle initially at rest decays into two spinning particles racing off in opposite directions (they have to be in opposite directions to conserve momentum). We catch one and find it spinning (from our point of view) clockwise. To conserve angular momentum, the other particle must be spinning anticlockwise - and indeed, when we get around to detecting it, we find that is is doing just that. Collapsing the wavefunction of one particle simultaneously collapses that of the other particle, _now matter how far away it may be at the time_. _That_ is a nonlocal interaction. You could argue that the particles had a well-defined spin all along, and so it should be no surprise that they happen to cancel out to satisfy conservation laws. Unfortunately, experimental evidence (involving some extensions to the basic EPR idea that I won't bother going into at this point), say that this is not good enough. The Copenhagenists claim that this just proves that a physically objective description of reality is impossible. After all, if things did exist independent of observation, then they'd have to be able to communicate at speeds faster than light - there have to be nonlocal interactions. That's silly, ergo an objectively physical reality is impossible. A realist contends instead that the Universe does exist independent of observers - and is prepared to accept nonlocal interactions as being necessary to bind said objective reality together. The "parallel worlds" model is an example of a realist universe. Every possible outcome of a quantum event is represented by a parallel universe, each following the consequences of one particular outcome. The nonlocal interaction is between these universes and decides which universe contains which possible outcome. Another is one I'm not at all sure what to call: The only way we can check to see that all conservation laws have been adhered to when we measure the spinning of these particles, is to measure both of them and bring the results together for comparison. This takes time - the act of transferring information is limited to the speed of light (nonlocal interactions may be instantaneous, but they can't communicate anything watches synchronised in advance can't do). So by the time we compare the spins of both particles, sufficient time has passed for all the relevant information to be moved about the experimental setup at the speed of light. Yeah, but that's _after_ the experiment's carried out! It's a bit late _now_ for the particles to agree on which way they're spinning. So? I said that a nonlocal interaction was needed, and here it comes: at the point the two measurements are compared, a signal travels (at light speed) _backwards in time_, to inform the two particles what the outcome of the experiment will be. If the two measurements are not compared, then no one will be any the wiser, so no signal need be sent back. What's a "comparison"? Any quantum event that is determined by the values of both quantities being compared. This includes the events that result from human eyeballs seeing the records printed by the detection apparatus regarding the spins of both particles, but could just as easily be the event of both particles - after having been reflected back towards each other - colliding. So every quantum event in the universe is not only a consequence of every event in its past (limited by the speed of light) but is further determined by every event which is a consequence of _it_. It makes causality time-symmetric. Anything can happen, so long as the law is found to be satisfied when a comparison between related events is made. But it's still useless for precognition. Morgan L. Owens _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Thu May 13 09:46:52 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id IAA19030 for philofractal-list; Thu, 13 May 1999 08:46:46 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from mtiwmhc06.worldnet.att.net (mtiwmhc06.worldnet.att.net [204.127.131.41]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id IAA18832; Thu, 13 May 1999 08:06:35 -0500 Received: from default ([12.74.100.181]) by mtiwmhc06.worldnet.att.net (InterMail v03.02.07 118 124) with SMTP id <19990513130236.CZXZ567@default>; Thu, 13 May 1999 13:02:36 +0000 Message-ID: <373ACD61.3161@Worldnet.att.net> Date: Thu, 13 May 1999 08:02:25 -0500 From: "Paul.N.Lee" Organization: Nahee Enterprises X-Mailer: Mozilla 3.04Gold (Win95; U) MIME-Version: 1.0 To: philofractal@icd.com CC: fractal-art@icd.com Subject: Re: [philofractal] FOTD 13-05-99 (Heart Land) (c) References: <1.5.4.16.19990513015256.2adfb3b8@pop.mindspring.com> Content-Type: text/plain; charset=iso-8859-2 Content-Transfer-Encoding: 7bit Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com Jim Muth wrote: > > The "Fractal of the Day" is in its 26th month and > showing no signs of slowing down. The "counter" for the January 1999 FOTD webpage of your images has over 3,889 "hits", with February coming in at over 2,085. Some of the most viewed images have been: http://home.att.net/~Paul.N.Lee/FotD/FotD_99-01-21.html - 192 "hits" http://home.att.net/~Paul.N.Lee/FotD/FotD_99-01-18.html - 166 "hits" http://home.att.net/~Paul.N.Lee/FotD/FotD_99-02-01.html - 165 "hits" http://home.att.net/~Paul.N.Lee/FotD/FotD_99-01-23.html - 151 "hits" > > There is an old short story titled "He Who Shrank". > The story is about a man who begins shrinking and > can't stop. "He Who Shrank" by Henry Hasse ("Amazing" Aug.1936), a novella in "Famous Science Fiction Stores: Adventures in Time and Space", edited by Raymond Healy and J. Frances McComas. (Which is Cliff Pickover's 3rd favorite book.) http://www.sff.net/locus/s346.html#A6794.2 P.N.L. -------------------------------------------------------------- http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Thu May 13 10:46:42 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id JAA19333 for philofractal-list; Thu, 13 May 1999 09:46:47 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp0.mindspring.com (smtp0.mindspring.com [207.69.200.30]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id JAA19103 for ; Thu, 13 May 1999 09:01:30 -0500 Received: from default (user-38ldh8t.dialup.mindspring.com [209.86.197.29]) by smtp0.mindspring.com (8.8.5/8.8.5) with SMTP id JAA07970 for ; Thu, 13 May 1999 09:57:53 -0400 (EDT) From: "Jason Hine" To: Subject: Re: [philofractal] FOTD 13-05-99 (Heart Land) (c) Date: Thu, 13 May 1999 06:38:30 -0700 Message-ID: <01be9d45$e378c680$1dc556d1@default> MIME-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 4.71.1712.3 X-MimeOLE: Produced By Microsoft MimeOLE V4.71.1712.3 Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com Jim Muth laments: >Even today, quantum mechanics is perilously near this stage. We >have the QM equations, and we know that they work. But we don't >know why they work. We lack a sensible corresponding physical >model. Indeed, we now know that a totally accurate physical >model of an atom is impossible. The reason that QM works so well is because it trancends the objective realities of the particles involved, and focuses on the _relationships_ that exist... indeed, the diagrams scientists draw to describe interactions in QM consist entirely of relationships; particles (and the preoperties thereof) are more like side-effects than anything else. This is obviously not how we experience the universe - we see separate entities, smell distinct smells, hear distinct notes. When I place a book on a table, I consider the facts of the book and the table much more important than the spatial relationship between them. I don't consider at all the fact that they were both once trees; that the molecules of both once comprised living cells which used nearly identical processes to metabolize food; that the atoms of both were among those which coalesced from the proto-Solar System to form the Earth; that the energy in each's particles was once one in the pre-Big Bang time (maybe). But these relationships do exist, and QM tells us that, though the effect might be undetectable due to the "static" of other relationships that have formed more recently, there are effects nonetheless from these ancient interactions. Could there be a huge number of uncollapsed wavefunctions in the natural world? Could the universe have a tendency toward producing uncollapsed wavefunctions? Could this be a new way of thinking about the reason life arose? Our memory is the only "sense" we have that can detect these relationships in day-to-day life - we can notice how things change over time. But if our five "regular" senses are coarse detectors in some respects, I'd have to say that memory is even worse. Hmm... if a scientist notices the outcome of a quantum experiment, and then forgets what the outcome was, does the wavefunction un-collapse? I'd have to say no. Just my two cent's worth, Jason "got my Star Wars tickets" Hine _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Thu May 13 14:46:49 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id NAA21238 for philofractal-list; Thu, 13 May 1999 13:46:37 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp4.mindspring.com (smtp4.mindspring.com [207.69.200.64]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id NAA21022 for ; Thu, 13 May 1999 13:13:52 -0500 Received: from LOCALNAME (user-2ivei0e.dialup.mindspring.com [165.247.72.14]) by smtp4.mindspring.com (8.8.5/8.8.5) with SMTP id OAA21883 for ; Thu, 13 May 1999 14:10:08 -0400 (EDT) Date: Thu, 13 May 1999 14:10:08 -0400 (EDT) Message-Id: <1.5.4.16.19990513141103.334f52bc@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] Re: FOTD 13-05-99 (Heart Land) Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com Morgan Owens Wrote: >Another [quantum interpretation]is one I'm not at all sure what to call: >So? I said that a nonlocal interaction was needed, and here it >comes: at the point the two measurements are compared, a signal >travels (at light speed) _backwards in time_, to inform the two >particles what the outcome of the experiment will be. >So every quantum event in the universe is not only a >consequence of every event in its past (limited by the speed of >light) but is further determined by every event which is a >consequence of _it_. >It makes causality time-symmetric. Anything can happen, so long >as the law is found to be satisfied when a comparison between >related events is made. REPLY----------------------------------------------------- This appears to be John Cramer's transactional interpretation of QM, which in my opinion is one of the best, since it includes elements of relativity and makes at least a modicum of sense. True, it stretches the scientific method a bit by supposing unobservable signals that travel backward in time, but it shows atoms to be real even when no one is looking. It could be very useful, because we make the best progress on problems that we can most clearly visualize in a physical way. The feature of the transactional interpretation that puts me off is the two-way causality, which means that at the quantum level at least, reality is super-deterministic. If causality works in the opposite direction, then at the quantum level it is no more possible to change the future than it is to change the past. If this super-determinism is ever shown to extend to the macroscopic level, there goes free will and here comes fatalism. No criminal can be considered guilty, because he had no choice but to commit his crime. We might as well give up medicine, because the time every person will die has been fixed since the moment the universe came into existence. It would be both wrong and futile to try to change the time of death in either direction. Also, if the future is pre-determined at the quantum level, it is only a matter of time before some clever thinker imagines a way of rigging a theoretical experiment to presumably tap into that already-existing future, and transfer the knowledge to the everyday level. I wonder how long it will be before the first quantum fortune-teller goes into business. (If they have not already done so.) In his book, "Schrodinger's Kittens", John Gribbin, admits that all interpretations of QM are myths, crutches to help us imagine what is going on at the quantum level, and thereby make testable predictions. IMO, everything is in a sense a myth. The common-sense physical world is a myth -- the way of seeing reality that offered primitive man the best chance of survival. It is up to the individual to decide which myths to consider real. If the physical universe alone is considered real, science and the scientific method results. If the worlds within our minds are also considered real, then religion, mysticism, shamanism, occultism, etc. become valid disciplines. But what is reality really like? That might be the ultimate unanswerable question. FOTD and a reply to Jason in 12 hours or so. Jim Muth jamth@mindspring.com _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Fri May 14 01:09:02 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id AAA25636 for philofractal-list; Fri, 14 May 1999 00:08:57 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from smtp5.mindspring.com (smtp5.mindspring.com [207.69.200.82]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id XAA25352; Thu, 13 May 1999 23:25:05 -0500 Received: from LOCALNAME (user-2iveins.dialup.mindspring.com [165.247.74.252]) by smtp5.mindspring.com (8.8.5/8.8.5) with SMTP id AAA28780; Fri, 14 May 1999 00:21:12 -0400 (EDT) Date: Fri, 14 May 1999 00:21:12 -0400 (EDT) Message-Id: <1.5.4.16.19990514001918.2ae7bb90@pop.mindspring.com> X-Sender: jamth@pop.mindspring.com X-Mailer: Windows Eudora Light Version 1.5.4 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: philofractal@icd.com From: Jim Muth Subject: [philofractal] FOTD 14-05-99 (The Cobra Strikes) (c) Cc: fractal-art@icd.com Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com FOTD -- May 14, 1999 Fractal enthusiasts, visionaries, and just plain curious: Today's fractal reminds me of either a backward question mark or a king cobra, raised and ready to strike. Since a striking cobra is more dramatic, I named the picture "The Cobra Strikes". The formula I used to draw the image is number six in the series of 12 MandNewt formulas. This formula sets such a ridiculously tiny cutoff value for that breakdown begins before cutoff is reached. The result is the haze of dots that surrounds the head and neck of the cobra. Of course, the higher the resolution, the better but slower the image will turn out. The original purpose of these formulas is long ago forgotten, but whatever the purpose was, it couldn't possibly have been as prolific as what resulted. Today's picture is not pretty. It has a restless, sinister effect, a bit muddy in places, but striking even from a distance. The coiled serpent draws in under an hour. The venomous reptile may be seen even quicker by downloading the picture file from: or from the WWW at Paul lee's web site: The fractal weather was overcast, with a temperature of 68F 20C, and a northeast wind off the North Atlantic -- a perfect day for fractaling and philosophizing. I got most of the near-philosophy out of me in an earlier post to the philofractal list. And there is a letter from Jason that I wanted to reply to. But that letter is unavailable in another mailbox over at a Fractal Central branch office. (Just like all Gaul, Fractal Central is divided into three parts!) Well, I'll have more philosophy to offer tomorrow anyway, when I've regcharged my philosophical fractal energies. Until 24 hours from now, take care, and be on the lookout for the Great Fractal. Jim Muth jamth@mindspring.com START FORMULA============================================= MandNewt06 {; Jim Muth z=c=(pixel*p1): a=z^3+(c-p2)*z-c b=p3*z^2+c-1 z=z-1*a/b .000000000000000000000000000001 <= |a| } END FORMULA=============================================== START PARAMETER FILE====================================== The_Cobra_Strikes { ; 0:08:08.29, p233, 640x480 reset=1960 type=formula formulafile=mandnewt.frm formulaname=MandNewt06 passes=1 center-mag=27.4397\ /0/0.01885867 params=-0.0574/-0.2341/5.1216/-4.2192\ /3.0159/2.4913 float=y maxiter=340 bailout=25 inside=bof60 logmap=yes symmetry=none periodicity=0 colors=000aDH<34>u8`y5c<27>WQENOH<9>vY3<22>jNjjNkkP\ j<25>ptYpuYotZ<58>YQ_`Sa<34>49P38P26Q<11>3DN3EN3EN4\ EM4DL3DK2CJ0CI<9>078 } END PARAMETER FILE======================================== START 19.6 PARAMETER-FORMULA FILE========================= The_Cobra_Strikes { ; 0:08:08.29, p233, 640x480 reset=1960 type=formula formulafile=mandnewt.frm formulaname=MandNewt06 passes=1 center-mag=27.4397\ /0/0.01885867 params=-0.0574/-0.2341/5.1216/-4.2192\ /3.0159/2.4913 float=y maxiter=340 bailout=25 inside=bof60 logmap=yes symmetry=none periodicity=0 colors=000aDH<34>u8`y5c<27>WQENOH<9>vY3<22>jNjjNkkP\ j<25>ptYpuYotZ<58>YQ_`Sa<34>49P38P26Q<11>3DN3EN3EN4\ EM4DL3DK2CJ0CI<9>078 } frm:MandNewt06 {; Jim Muth z=c=(pixel*p1): a=z^3+(c-p2)*z-c b=p3*z^2+c-1 z=z-1*a/b .000000000000000000000000000001 <= |a| } END 19.6 PARAMETER-FORMULA FILE=========================== _______ ______ _____ ____ ___ __ _ post: send message to philofractal@icd.com unsub: send "unsubscribe" to philofractal-request@icd.com admin: send comments to philofractal-owner@icd.com From owner-philofractal@icd.com Fri May 14 01:15:21 1999 Received: (from majordomo@localhost) by rock.icd.com (8.9.1/8.9.1) id AAA25632 for philofractal-list; Fri, 14 May 1999 00:08:52 -0500 X-Authentication-Warning: rock.icd.com: majordomo set sender to owner-philofractal@icd.com using -f Received: from bo.nznet.gen.nz (ns1.nznet.gen.nz [203.167.232.34]) by rock.icd.com (8.9.1/8.9.1) with ESMTP id XAA25541 for ; Thu, 13 May 1999 23:50:35 -0500 Received: from packrat.nznet.gen.nz (ms2-17.nznet.gen.nz [203.167.232.147]) by bo.nznet.gen.nz (8.8.7/8.8.8) with SMTP id QAA10059 for ; Fri, 14 May 1999 16:52:57 +1200 Message-Id: <3.0.3.32.19990514164527.006fa560@mail.nznet.gen.nz> X-Sender: packrat@mail.nznet.gen.nz X-Mailer: QUALCOMM Windows Eudora Light Version 3.0.3 (32) Date: Fri, 14 May 1999 16:45:27 +1200 To: philofractal@icd.com From: "Morgan L. Owens" Subject: Re: [philofractal] Re: FOTD 13-05-99 (Heart Land) In-Reply-To: <1.5.4.16.19990513141103.334f52bc@pop.mindspring.com> Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Sender: owner-philofractal@icd.com Precedence: bulk Reply-To: philofractal@icd.com At 14:10 13/05/99 -0400, you wrote: > >This appears to be John Cramer's transactional interpretation of >QM, > The name does ring a bell ... I'll have to look it up. >True, it stretches the scientific method a bit by supposing >unobservable signals that travel backward in time, but it shows >atoms to be real even when no one is looking. > Well, like I said: objective reality _or_ nonlocal interactions - you can't have both. I'm more prepared to accept that General Relativity has a hole in it somewhere than give up on the universe's existing! One mildly amusing thing that occurred to me shortly after writing: a particle travelling backwards in time looks exactly like the corresponding antiparticle travelling forwards in time. A photon is its own antiparticle, so a photon travelling backwards in time looks exactly like a photon travelling forwards in time - so from our point of view (any frame of reference independent of the photon's) the two are indistinguishable. Being massless, a photon travels at the speed of light so in the photon's frame of reference the trip takes zero time. So from the photon's point of view as well the two are _still_ indistinguishable. Shall we hypothesise a massless particle that is its own antiparticle that is exchanged between events? (This would make it a _virtual_ particle.) Or can we get away with one of the already-known ones - in which case my favourite would be the graviton. >It could be very >useful, because we make the best progress on problems that we >can most clearly visualize in a physical way. > >The feature of the transactional interpretation that puts me off >is the two-way causality, which means that at the quantum level >at least, reality is super-deterministic. > >If causality works in the opposite direction, then at the >quantum level it is no more possible to change the future than >it is to change the past. If this super-determinism is ever >shown to extend to the macroscopic level, there goes free will >and here comes fatalism. No criminal can be considered guilty, >because he had no choice but to commit his crime. We might as >well give up medicine, because the time every person will die >has been fixed since the moment the universe came into >existence. It would be both wrong and futile to try to change >the time of death in either direction. > "I'm sorry your honour: the future forced me to commit the crime." "How do you know?" Like I said, anything consistent goes. Events that are never compared don't have to satisfy physical law, and there is nothing in the events that determines when and how any comparisons that do happen are to occur. "Hey, the polarisation of these photons don't match!" "Um, I _did_ send one through a polarising filter..." "Ah, that explains it then." >Also, if the future is pre-determined at the quantum level, it >is only a matter of time before some clever thinker imagines a >way of rigging a theoretical experiment to presumably tap into >that already-existing future, and transfer the knowledge to the >everyday level. I wonder how long it will be before the first >quantum fortune-teller goes into business. (If they have not >already done so.) > Following are two possible records of a series of quantum measurements. In one a signal (a particular series of events) from the future has been embedded. If the signal is received, the events will take place, if it's not received the events don't take place. Which one contains the signal? Signal 1: 10100101100110111101100010101100 Signal 2: 11001100000011010100111011000101 To extract the signal from the future, you have to find a way of filtering out every other event that will happen in the future of your recording apparatus. Consider the "one-time pad" cipher system. >In his book, "Schrodinger's Kittens", John Gribbin, admits that >all interpretations of QM are myths, crutches to help us imagine >what is going on at the quantum level, and thereby make testable >predictions. > >IMO, everything is in a sense a myth. The common-sense physical >world is a myth -- the way of seeing reality that offered >pr